3420:
of the digit 1. Any terminating expansion in the ternary system is equivalent to the expression that is identical up to the term preceding the last non-zero term followed by the term one less than the last non-zero term of the first expression, followed by an infinite tail of twos. For example: 0.1020 is equivalent to 0.1012222... because the expansions are the same until the "two" of the first expression, the two was decremented in the second expansion, and trailing zeros were replaced with trailing twos in the second expression.
3328:
3419:
conveniently. Additionally, it turns out that the ternary representation is useful for defining the Cantor set and related point sets, because of the way the Cantor set is constructed. The Cantor set consists of the points from 0 to 1 that have a ternary expression that does not contain any instance
3471:
Simulation of ternary computers using binary computers, or interfacing between ternary and binary computers, can involve use of binary-coded ternary (BCT) numbers, with two or three bits used to encode each trit. BCT encoding is analogous to
3331:
Use of ternary numbers to balance an unknown integer weight from 1 to 40 kg with weights of 1, 3, 9 and 27 kg (4 ternary digits actually gives 3 = 81 possible combinations: −40 to +40, but only the positive values are
3909:
3569:
3776:
3476:(BCD) encoding. If the trit values 0, 1 and 2 are encoded 00, 01 and 10, conversion in either direction between binary-coded ternary and binary can be done in
4104:
3408:(which is sometimes used as an alternative by some record keepers). In this usage, only the fractional part of the number is written in ternary form.
712:
4475:
4109:
432:
4099:
4094:
3752:
4082:
3983:
3835:
3363:
reference at all. Where the signal is usually grounded to a certain reference, or at a certain voltage level, the state is said to be high
4531:
265:
3654:"Hybrid signed–digit number systems: a unified framework for redundant number representations with bounded carry propagation chains"
3936:
3341:
56:
4233:
3452:
4350:
4155:
4087:
4049:
3700:
3661:
499:
3880:
705:
280:
4526:
4250:
4180:
4028:
3459:, is sometimes used in low-level software and hardware to accomplish fast addition of integers because it can eliminate
625:
3698:
Frieder, Gideon; Luk, Clement (February 1975). "Algorithms for Binary Coded
Balanced and Ordinary Ternary Operations".
635:
4505:
3456:
452:
3386:. For example, if a player pitched all of the 4th, 5th and 6th innings, plus achieving 2 outs in the 7th inning, his
3444:. It has been used for some computing systems because of this efficiency. It is also used to represent three-option
4536:
4260:
4128:
512:
4438:
4390:
4302:
4280:
4275:
4203:
4069:
3439:
3432:
608:
377:
3307:(base 27, each digit is three ternary digits) can be used for compact representation of ternary, similar to how
4312:
3976:
3481:
904:(six digits). However, they are still far less compact than the corresponding representations in bases such as
698:
25:
4465:
4380:
3876:
3735:
Parhami, Behrooz; McKeown, Michael (2013-11-03). "Arithmetic with binary-encoded balanced ternary numbers".
3367:
because it is open and serves its own reference. Thus, the actual voltage level is sometimes unpredictable.
3336:
In certain analog logic, the state of the circuit is often expressed ternary. This is most commonly seen in
688:
472:
69:
4208:
4064:
3670:
3412:
288:
4198:
4173:
3436:
3428:
3316:
851:
490:
3345:
2314:
in decimal); but a major drawback is that, in turn, ternary does not offer a finite representation for
4000:
3827:
3473:
3364:
3349:
917:
804:
585:
446:
439:
320:
3675:
4470:
4448:
4375:
4228:
4220:
4140:
3969:
3593:
814:
most often refers to a system in which the three digits are all non–negative numbers; specifically
667:
532:
483:
295:
227:
82:
43:
4453:
4433:
4385:
4360:
4145:
4114:
3888:
3770:
3758:
3717:
3460:
580:
333:
170:
165:
112:
3950:
3327:
4340:
4270:
4245:
4059:
4054:
3831:
3748:
2311:
662:
652:
640:
620:
575:
570:
506:
338:
310:
217:
150:
140:
127:
92:
87:
4485:
4370:
4168:
3901:
3740:
3709:
3680:
3536:
3493:
835:
827:
797:
731:
565:
459:
212:
200:
145:
135:
102:
77:
3956:
4490:
4355:
4307:
4240:
3940:
3633:
Soltanifar, Mohsen (2006). "A Different
Description of A Family of Middle–α Cantor Sets".
3477:
3387:
3304:
2291:
909:
781:
677:
647:
590:
560:
545:
305:
273:
245:
222:
205:
64:
3653:
657:
3570:"A complete beginner's guide to baseball stats: Pitching statistics, and what they mean"
2405:) is not representable exactly (that would need e.g. decimal); nor is one-sixth (senary
2310:
as same as senary (as opposed to its cumbersome representation as an infinite string of
4443:
4265:
4255:
4163:
3806:
3379:
3378:), to denote fractional parts of an inning. Since the team on offense is allowed three
3353:
847:
757:
672:
615:
595:
550:
423:
155:
122:
107:
33:
4520:
4365:
3933:
3541:
3512:
3424:
2370:
478:
367:
300:
240:
175:
117:
97:
3721:
3359:). In this configuration the output of the circuit is actually not connected to any
4322:
4297:
3791:
3762:
2367:
858:
630:
555:
3945:
3852:
3821:
4500:
4495:
4345:
4292:
4119:
3547:
3312:
600:
465:
417:
407:
3744:
908:– see below for a compact way to codify ternary using nonary (base 9) and
4405:
4400:
4317:
4285:
4190:
4133:
3416:
2363:
823:
819:
815:
769:
402:
160:
3370:
A rare "ternary point" in common use is for defensive statistics in
American
4480:
4458:
4415:
4410:
4077:
4033:
3992:
3713:
412:
3382:, each out is considered one third of a defensive inning and is denoted as
4395:
3905:
3897:
3371:
3448:, such as phone menu systems, which allow a simple path to any branch.
3411:
Ternary numbers can be used to convey self-similar structures like the
3375:
3360:
905:
855:
397:
382:
3851:
Brousentsov, N. P.; Maslov, S. P.; Ramil
Alvarez, J.; Zhogolev, E. A.
3684:
831:
3527:
865:
387:
3826:. First IFIP WG 9.7 Conference, SoRuCom 2006. Petrozavodsk, Russia:
3532:
3497:
3326:
3308:
3293:(3, 3) = 3 − 1 = 26 = 2 × 3 + 2 × 3 + 2 × 3 = 18 + 6 + 2
773:
392:
354:
315:
4013:
3515:
3337:
3965:
3614:
Soltanifar, Mohsen (2006). "On A sequence of cantor
Fractals".
4008:
3505:
891:
777:
746:
3961:
3953: – includes fractional part, from Maths Is Fun
3853:"Development of ternary computers at Moscow State University"
850:
in ternary do not get uncomfortably lengthy as quickly as in
740:
749:
3737:
2013 Asilomar
Conference on Signals, Systems and Computers
3455:
called a binary signed-digit number system, a form of
3739:. Pacific Grove, California, US. pp. 1130–1133.
3303:
Nonary (base 9, each digit is two ternary digits) or
743:
737:
4424:
4333:
4219:
4189:
4154:
4042:
3999:
3957:
Gideon
Frieder's replacement ternary numeral system
734:
2979:digits, all of which are the maximal digit value
2944:Sum of the digits in ternary as opposed to binary
2373:of the base; as with base two, one-tenth (decimal
3946:The ternary calculating machine of Thomas Fowler
2294:, ternary offers a convenient way to represent
3977:
3820:Impagliazzo, John; Proydakov, Eduard (2006).
3616:Rose Hulman Undergraduate Mathematics Journal
3299:Compact ternary representation: base 9 and 27
706:
8:
3900:, the Scientific Research Society: 490–494.
3823:Perspectives on Soviet and Russian Computing
3423:Ternary is the integer base with the lowest
3137: − ... − b − 1
1445:Numbers from 0 to 3 − 1 in standard ternary
826:, the adjective also lends its name to the
3984:
3970:
3962:
3775:: CS1 maint: location missing publisher (
3635:American Journal of Undergraduate Research
713:
699:
49:
20:
3674:
834:, 0 and +1, used in comparison logic and
3484:supporting BCT arithmetic is available.
3390:column for that game would be listed as
2441:
1911:
1442:
914:
3560:
3348:. The output is said to either be low (
32:
3807:"Ternary Data Types for C Programmers"
3792:"Binary Coded Ternary and its Inverse"
3768:
3435:. This is due to its proximity to the
3504:to be six trits or approximately 9.5
7:
3508:(holding more information than the
3288:For a three-digit ternary number,
2948:The value of a binary number with
14:
3652:Phatak, D. S.; Koren, I. (1994).
3805:Jones, Douglas W. (2015-12-29).
803: 3 (about 1.58496) bits of
730:
3915:from the original on 2019-10-30
3790:Jones, Douglas W. (June 2016).
3568:Ashley MacLennan (2019-01-09).
3453:redundant binary representation
3701:IEEE Transactions on Computers
3662:IEEE Transactions on Computers
830:system; comprising the digits
1:
4050:Arbitrary-precision or bignum
3596:. MLB (Major League Baseball)
3315:systems are used in place of
796:). One trit is equivalent to
2876:
2820:
2752:
2681:
2448:
2255:
2220:
2175:
2112:
2052:
2018:
1998:
1978:
1948:
1918:
1869:
1837:
1760:
1728:
1692:
1660:
1618:
1586:
1550:
1518:
1481:
1449:
3457:signed-digit representation
3342:transistor–transistor logic
4553:
4532:Positional numeral systems
4023:
3879:(November–December 2001).
3745:10.1109/ACSSC.2013.6810470
2049:
1725:
1583:
433:Non-standard radices/bases
4391:Strongly typed identifier
3594:"Stats - Team - Pitching"
842:Comparison to other bases
2959:Similarly, for a number
4466:Parametric polymorphism
3951:Ternary Base Conversion
3714:10.1109/T-C.1975.224188
2952:bits that are all 1 is
689:List of numeral systems
3427:, followed closely by
3340:circuits, and also in
3333:
1914:Powers of 3 in ternary
877:corresponds to binary
3437:mathematical constant
3330:
57:Hindu–Arabic numerals
16:Base-3 numeral system
3906:10.1511/2001.40.3268
3474:binary-coded decimal
3467:Binary-coded ternary
3394:, the equivalent of
2444:Fractions in ternary
918:multiplication table
586:Prehistoric counting
362:Common radices/bases
44:Place-value notation
4527:Computer arithmetic
4471:Primitive data type
4376:Recursive data type
4229:Algebraic data type
4105:Quadruple precision
3413:Sierpinski triangle
2446:
1916:
1447:
920:
846:Representations of
533:Sign-value notation
4434:Abstract data type
4115:Extended precision
4074:Reduced precision
3939:2011-05-14 at the
3934:Ternary Arithmetic
3889:American Scientist
3374:(usually just for
3352:), high, or open (
3334:
2442:
1912:
1443:
915:
189:East Asian systems
4537:Ternary computers
4514:
4513:
4246:Associative array
4110:Octuple precision
3754:978-1-4799-2390-8
3685:10.1109/12.295850
3494:ternary computers
3346:totem-pole output
2939:
2938:
2362:, etc.), because
2286:
2285:
1902:
1901:
1439:
1438:
894:) and to ternary
836:ternary computers
776:. Analogous to a
723:
722:
522:
521:
4544:
4486:Type constructor
4371:Opaque data type
4303:Record or Struct
4100:Double precision
4095:Single precision
3986:
3979:
3972:
3963:
3923:
3921:
3920:
3914:
3885:
3863:
3862:
3860:
3859:
3848:
3842:
3841:
3837:978-3-64222816-2
3817:
3811:
3810:
3802:
3796:
3795:
3787:
3781:
3780:
3774:
3766:
3732:
3726:
3725:
3695:
3689:
3688:
3678:
3658:
3649:
3643:
3642:
3630:
3624:
3623:
3611:
3605:
3604:
3602:
3601:
3590:
3584:
3583:
3581:
3580:
3565:
3537:ternary computer
3478:logarithmic time
3407:
3406:
3402:
3399:
3294:
3284:
3278:
3261:
3259:
3257:
3256:
3250:
3247:
3242: − 1)(
3232:
3215:
3186:
3184:
3182:
3181:
3175:
3172:
3155:
3138:
3120:
3096:
3087:
3070:
3057: − 1)(
3052:
3035:
2986:, we can write:
2985:
2955:
2935:
2929:
2923:
2914:
2905:
2899:
2887:
2873:
2864:
2858:
2846:
2837:
2817:
2811:
2805:
2799:
2793:
2784:
2778:
2772:
2763:
2749:
2743:
2737:
2731:
2722:
2716:
2710:
2704:
2698:
2689:
2677:
2675:
2674:
2671:
2668:
2658:
2656:
2655:
2652:
2649:
2639:
2637:
2636:
2633:
2630:
2620:
2618:
2617:
2614:
2611:
2601:
2599:
2598:
2595:
2592:
2582:
2580:
2579:
2576:
2573:
2563:
2561:
2560:
2557:
2554:
2544:
2542:
2541:
2538:
2535:
2525:
2523:
2522:
2519:
2516:
2506:
2504:
2503:
2500:
2497:
2487:
2485:
2484:
2481:
2478:
2468:
2466:
2465:
2462:
2459:
2447:
2436:
2434:
2433:
2430:
2427:
2420:
2418:
2417:
2414:
2411:
2404:
2402:
2401:
2398:
2395:
2388:
2386:
2385:
2382:
2379:
2361:
2359:
2358:
2355:
2352:
2345:
2343:
2342:
2339:
2336:
2329:
2327:
2326:
2323:
2320:
2312:recurring digits
2309:
2307:
2306:
2303:
2300:
2292:rational numbers
2282:
2277:
2272:
2267:
2262:
2252:
2251:
2244:
2243:
2236:
2235:
2217:
2216:
2209:
2208:
2201:
2200:
2193:
2192:
2185:
2184:
2172:
2171:
2168:
2165:
2158:
2157:
2154:
2151:
2144:
2143:
2140:
2133:
2132:
2129:
2122:
2121:
2109:
2108:
2105:
2102:
2095:
2094:
2091:
2084:
2083:
2080:
2073:
2072:
2069:
2062:
2061:
2045:
2040:
2035:
2030:
2025:
1975:
1974:
1967:
1966:
1945:
1944:
1937:
1936:
1917:
1834:
1833:
1826:
1825:
1818:
1817:
1810:
1809:
1802:
1801:
1794:
1793:
1786:
1785:
1778:
1777:
1770:
1769:
1657:
1656:
1649:
1648:
1515:
1514:
1448:
1435:
1434:
1427:
1426:
1419:
1418:
1411:
1410:
1403:
1402:
1395:
1394:
1387:
1386:
1366:
1365:
1358:
1357:
1350:
1349:
1342:
1341:
1334:
1333:
1326:
1325:
1302:
1301:
1294:
1293:
1286:
1285:
1278:
1277:
1270:
1269:
1262:
1261:
1238:
1237:
1230:
1229:
1222:
1221:
1214:
1213:
1206:
1205:
1179:
1178:
1171:
1170:
1163:
1162:
1155:
1154:
1125:
1124:
1117:
1116:
1109:
1108:
1076:
1075:
921:
912:(base 27).
900:
899:
886:
885:
882:
873:
872:
828:balanced ternary
756:
755:
752:
751:
748:
745:
742:
739:
736:
715:
708:
701:
504:
488:
470:
460:balanced ternary
457:
444:
50:
21:
4552:
4551:
4547:
4546:
4545:
4543:
4542:
4541:
4517:
4516:
4515:
4510:
4491:Type conversion
4426:
4420:
4356:Enumerated type
4329:
4215:
4209:null-terminated
4185:
4150:
4038:
3995:
3990:
3941:Wayback Machine
3930:
3918:
3916:
3912:
3883:
3875:
3872:
3870:Further reading
3867:
3866:
3857:
3855:
3850:
3849:
3845:
3838:
3819:
3818:
3814:
3804:
3803:
3799:
3789:
3788:
3784:
3767:
3755:
3734:
3733:
3729:
3697:
3696:
3692:
3676:10.1.1.352.6407
3656:
3651:
3650:
3646:
3632:
3631:
3627:
3613:
3612:
3608:
3599:
3597:
3592:
3591:
3587:
3578:
3576:
3567:
3566:
3562:
3557:
3524:
3490:
3480:. A library of
3469:
3404:
3400:
3397:
3395:
3388:innings pitched
3325:
3323:Practical usage
3305:septemvigesimal
3301:
3289:
3283: − 1.
3265:
3264:
3251:
3248:
3246: − 1)
3237:
3236:
3234:
3219:
3218:
3210: − 1)
3194:
3176:
3173:
3167:
3166:
3164:
3159:
3142:
3124:
3100:
3092: − 1)
3074:
3073:
3039:
3038:
3030: − 1)
3022: − 1)
3014: − 1)
3006: − 1)
2990:
2980:
2954:2 − 1
2953:
2946:
2933:
2927:
2921:
2912:
2903:
2897:
2885:
2871:
2862:
2856:
2844:
2835:
2815:
2809:
2803:
2797:
2791:
2782:
2776:
2770:
2761:
2747:
2741:
2735:
2729:
2720:
2714:
2708:
2702:
2696:
2687:
2672:
2669:
2666:
2665:
2663:
2653:
2650:
2647:
2646:
2644:
2634:
2631:
2628:
2627:
2625:
2615:
2612:
2609:
2608:
2606:
2596:
2593:
2590:
2589:
2587:
2577:
2574:
2571:
2570:
2568:
2558:
2555:
2552:
2551:
2549:
2539:
2536:
2533:
2532:
2530:
2520:
2517:
2514:
2513:
2511:
2501:
2498:
2495:
2494:
2492:
2482:
2479:
2476:
2475:
2473:
2463:
2460:
2457:
2456:
2454:
2431:
2428:
2425:
2424:
2422:
2415:
2412:
2409:
2408:
2406:
2399:
2396:
2393:
2392:
2390:
2383:
2380:
2377:
2376:
2374:
2356:
2353:
2350:
2349:
2347:
2340:
2337:
2334:
2333:
2331:
2324:
2321:
2318:
2317:
2315:
2304:
2301:
2298:
2297:
2295:
2280:
2275:
2270:
2265:
2260:
2249:
2247:
2241:
2239:
2233:
2231:
2214:
2212:
2206:
2204:
2198:
2196:
2190:
2188:
2182:
2180:
2169:
2166:
2163:
2161:
2155:
2152:
2149:
2147:
2141:
2138:
2136:
2130:
2127:
2125:
2119:
2117:
2106:
2103:
2100:
2098:
2092:
2089:
2087:
2081:
2078:
2076:
2070:
2067:
2065:
2059:
2057:
2043:
2038:
2033:
2028:
2023:
1972:
1970:
1964:
1962:
1942:
1940:
1934:
1932:
1831:
1829:
1823:
1821:
1815:
1813:
1807:
1805:
1799:
1797:
1791:
1789:
1783:
1781:
1775:
1773:
1767:
1765:
1654:
1652:
1646:
1644:
1512:
1510:
1432:
1430:
1424:
1422:
1416:
1414:
1408:
1406:
1400:
1398:
1392:
1390:
1384:
1382:
1363:
1361:
1355:
1353:
1347:
1345:
1339:
1337:
1331:
1329:
1323:
1321:
1299:
1297:
1291:
1289:
1283:
1281:
1275:
1273:
1267:
1265:
1259:
1257:
1235:
1233:
1227:
1225:
1219:
1217:
1211:
1209:
1203:
1201:
1176:
1174:
1168:
1166:
1160:
1158:
1152:
1150:
1122:
1120:
1114:
1112:
1106:
1104:
1073:
1071:
910:septemvigesimal
903:
897:
895:
889:
883:
880:
878:
876:
870:
868:
863:
854:. For example,
848:integer numbers
844:
801:
733:
729:
719:
683:
682:
605:
591:Proto-cuneiform
536:
535:
524:
523:
518:
517:
502:
486:
468:
455:
442:
429:
358:
357:
345:
344:
325:
285:
270:
261:
260:
251:
250:
232:
191:
190:
181:
180:
132:
74:
60:
59:
47:
46:
34:Numeral systems
17:
12:
11:
5:
4550:
4548:
4540:
4539:
4534:
4529:
4519:
4518:
4512:
4511:
4509:
4508:
4503:
4498:
4493:
4488:
4483:
4478:
4473:
4468:
4463:
4462:
4461:
4451:
4446:
4444:Data structure
4441:
4436:
4430:
4428:
4422:
4421:
4419:
4418:
4413:
4408:
4403:
4398:
4393:
4388:
4383:
4378:
4373:
4368:
4363:
4358:
4353:
4348:
4343:
4337:
4335:
4331:
4330:
4328:
4327:
4326:
4325:
4315:
4310:
4305:
4300:
4295:
4290:
4289:
4288:
4278:
4273:
4268:
4263:
4258:
4253:
4248:
4243:
4238:
4237:
4236:
4225:
4223:
4217:
4216:
4214:
4213:
4212:
4211:
4201:
4195:
4193:
4187:
4186:
4184:
4183:
4178:
4177:
4176:
4171:
4160:
4158:
4152:
4151:
4149:
4148:
4143:
4138:
4137:
4136:
4126:
4125:
4124:
4123:
4122:
4112:
4107:
4102:
4097:
4092:
4091:
4090:
4085:
4083:Half precision
4080:
4070:Floating point
4067:
4062:
4057:
4052:
4046:
4044:
4040:
4039:
4037:
4036:
4031:
4026:
4021:
4016:
4011:
4005:
4003:
3997:
3996:
3991:
3989:
3988:
3981:
3974:
3966:
3960:
3959:
3954:
3948:
3943:
3929:
3928:External links
3926:
3925:
3924:
3871:
3868:
3865:
3864:
3843:
3836:
3812:
3797:
3782:
3753:
3727:
3708:(2): 212–215.
3690:
3669:(8): 880–891.
3644:
3625:
3606:
3585:
3574:Bless You Boys
3559:
3558:
3556:
3553:
3552:
3551:
3544:
3539:
3530:
3523:
3520:
3489:
3486:
3468:
3465:
3324:
3321:
3300:
3297:
3286:
3285:
3262:
3255: − 1
3216:
3188:
3187:
3180: − 1
3171: − 1
3157:
3154: − 1
3140:
3122:
3098:
3071:
3036:
2984: − 1
2945:
2942:
2941:
2940:
2937:
2936:
2930:
2924:
2918:
2915:
2909:
2906:
2900:
2894:
2891:
2888:
2882:
2879:
2875:
2874:
2868:
2865:
2859:
2853:
2850:
2847:
2841:
2838:
2832:
2829:
2826:
2823:
2819:
2818:
2812:
2806:
2800:
2794:
2788:
2785:
2779:
2773:
2767:
2764:
2758:
2755:
2751:
2750:
2744:
2738:
2732:
2726:
2723:
2717:
2711:
2705:
2699:
2693:
2690:
2684:
2680:
2679:
2660:
2641:
2622:
2603:
2584:
2565:
2546:
2527:
2508:
2489:
2470:
2451:
2288:
2287:
2284:
2283:
2278:
2273:
2268:
2263:
2258:
2254:
2253:
2245:
2237:
2229:
2226:
2223:
2219:
2218:
2210:
2202:
2194:
2186:
2178:
2174:
2173:
2159:
2145:
2134:
2123:
2115:
2111:
2110:
2096:
2085:
2074:
2063:
2055:
2051:
2050:
2047:
2046:
2041:
2036:
2031:
2026:
2021:
2017:
2016:
2013:
2010:
2007:
2004:
2001:
1997:
1996:
1993:
1990:
1987:
1984:
1981:
1977:
1976:
1968:
1960:
1957:
1954:
1951:
1947:
1946:
1938:
1930:
1927:
1924:
1921:
1908:
1907:
1904:
1903:
1900:
1899:
1896:
1893:
1890:
1887:
1884:
1881:
1878:
1875:
1872:
1868:
1867:
1864:
1861:
1858:
1855:
1852:
1849:
1846:
1843:
1840:
1836:
1835:
1827:
1819:
1811:
1803:
1795:
1787:
1779:
1771:
1763:
1759:
1758:
1755:
1752:
1749:
1746:
1743:
1740:
1737:
1734:
1731:
1727:
1726:
1723:
1722:
1719:
1716:
1713:
1710:
1707:
1704:
1701:
1698:
1695:
1691:
1690:
1687:
1684:
1681:
1678:
1675:
1672:
1669:
1666:
1663:
1659:
1658:
1650:
1642:
1639:
1636:
1633:
1630:
1627:
1624:
1621:
1617:
1616:
1613:
1610:
1607:
1604:
1601:
1598:
1595:
1592:
1589:
1585:
1584:
1581:
1580:
1577:
1574:
1571:
1568:
1565:
1562:
1559:
1556:
1553:
1549:
1548:
1545:
1542:
1539:
1536:
1533:
1530:
1527:
1524:
1521:
1517:
1516:
1508:
1505:
1502:
1499:
1496:
1493:
1490:
1487:
1484:
1480:
1479:
1476:
1473:
1470:
1467:
1464:
1461:
1458:
1455:
1452:
1437:
1436:
1428:
1420:
1412:
1404:
1396:
1388:
1380:
1377:
1374:
1368:
1367:
1359:
1351:
1343:
1335:
1327:
1319:
1316:
1313:
1310:
1304:
1303:
1295:
1287:
1279:
1271:
1263:
1255:
1252:
1249:
1246:
1240:
1239:
1231:
1223:
1215:
1207:
1199:
1196:
1193:
1190:
1187:
1181:
1180:
1172:
1164:
1156:
1148:
1145:
1142:
1139:
1136:
1133:
1127:
1126:
1118:
1110:
1102:
1099:
1096:
1093:
1090:
1087:
1084:
1078:
1077:
1069:
1066:
1063:
1060:
1057:
1054:
1051:
1048:
1045:
1039:
1038:
1035:
1032:
1029:
1026:
1023:
1020:
1017:
1014:
1011:
1005:
1004:
1001:
998:
995:
992:
989:
986:
983:
980:
977:
971:
970:
965:
960:
955:
950:
945:
940:
935:
930:
925:
901:
887:
874:
861:
843:
840:
799:
758:numeral system
721:
720:
718:
717:
710:
703:
695:
692:
691:
685:
684:
681:
680:
675:
670:
665:
660:
655:
650:
645:
644:
643:
638:
633:
623:
618:
612:
611:
604:
603:
598:
593:
588:
583:
578:
573:
568:
563:
558:
553:
548:
542:
541:
540:Non-alphabetic
537:
531:
530:
529:
526:
525:
520:
519:
516:
515:
510:
497:
481:
476:
463:
450:
436:
435:
428:
427:
420:
415:
410:
405:
400:
395:
390:
385:
380:
375:
370:
364:
363:
359:
352:
351:
350:
347:
346:
343:
342:
336:
330:
329:
324:
323:
318:
313:
308:
303:
298:
292:
291:
289:Post-classical
284:
283:
277:
276:
269:
268:
262:
258:
257:
256:
253:
252:
249:
248:
243:
237:
236:
231:
230:
225:
220:
215:
210:
209:
208:
197:
196:
192:
188:
187:
186:
183:
182:
179:
178:
173:
168:
163:
158:
153:
148:
143:
138:
131:
130:
125:
120:
115:
110:
105:
100:
95:
90:
85:
80:
73:
72:
70:Eastern Arabic
67:
65:Western Arabic
61:
55:
54:
53:
48:
42:
41:
40:
37:
36:
30:
29:
15:
13:
10:
9:
6:
4:
3:
2:
4549:
4538:
4535:
4533:
4530:
4528:
4525:
4524:
4522:
4507:
4504:
4502:
4499:
4497:
4494:
4492:
4489:
4487:
4484:
4482:
4479:
4477:
4474:
4472:
4469:
4467:
4464:
4460:
4457:
4456:
4455:
4452:
4450:
4447:
4445:
4442:
4440:
4437:
4435:
4432:
4431:
4429:
4423:
4417:
4414:
4412:
4409:
4407:
4404:
4402:
4399:
4397:
4394:
4392:
4389:
4387:
4384:
4382:
4379:
4377:
4374:
4372:
4369:
4367:
4366:Function type
4364:
4362:
4359:
4357:
4354:
4352:
4349:
4347:
4344:
4342:
4339:
4338:
4336:
4332:
4324:
4321:
4320:
4319:
4316:
4314:
4311:
4309:
4306:
4304:
4301:
4299:
4296:
4294:
4291:
4287:
4284:
4283:
4282:
4279:
4277:
4274:
4272:
4269:
4267:
4264:
4262:
4259:
4257:
4254:
4252:
4249:
4247:
4244:
4242:
4239:
4235:
4232:
4231:
4230:
4227:
4226:
4224:
4222:
4218:
4210:
4207:
4206:
4205:
4202:
4200:
4197:
4196:
4194:
4192:
4188:
4182:
4179:
4175:
4172:
4170:
4167:
4166:
4165:
4162:
4161:
4159:
4157:
4153:
4147:
4144:
4142:
4139:
4135:
4132:
4131:
4130:
4127:
4121:
4118:
4117:
4116:
4113:
4111:
4108:
4106:
4103:
4101:
4098:
4096:
4093:
4089:
4086:
4084:
4081:
4079:
4076:
4075:
4073:
4072:
4071:
4068:
4066:
4063:
4061:
4058:
4056:
4053:
4051:
4048:
4047:
4045:
4041:
4035:
4032:
4030:
4027:
4025:
4022:
4020:
4017:
4015:
4012:
4010:
4007:
4006:
4004:
4002:
4001:Uninterpreted
3998:
3994:
3987:
3982:
3980:
3975:
3973:
3968:
3967:
3964:
3958:
3955:
3952:
3949:
3947:
3944:
3942:
3938:
3935:
3932:
3931:
3927:
3911:
3907:
3903:
3899:
3895:
3891:
3890:
3882:
3878:
3874:
3873:
3869:
3854:
3847:
3844:
3839:
3833:
3829:
3825:
3824:
3816:
3813:
3808:
3801:
3798:
3793:
3786:
3783:
3778:
3772:
3764:
3760:
3756:
3750:
3746:
3742:
3738:
3731:
3728:
3723:
3719:
3715:
3711:
3707:
3703:
3702:
3694:
3691:
3686:
3682:
3677:
3672:
3668:
3664:
3663:
3655:
3648:
3645:
3640:
3636:
3629:
3626:
3622:(1). Paper 9.
3621:
3617:
3610:
3607:
3595:
3589:
3586:
3575:
3571:
3564:
3561:
3554:
3550:
3549:
3545:
3543:
3542:Ternary logic
3540:
3538:
3534:
3531:
3529:
3526:
3525:
3521:
3519:
3517:
3514:
3511:
3507:
3503:
3499:
3495:
3487:
3485:
3483:
3479:
3475:
3466:
3464:
3462:
3458:
3454:
3449:
3447:
3443:
3442:
3438:
3434:
3430:
3426:
3425:radix economy
3421:
3418:
3414:
3409:
3393:
3389:
3385:
3381:
3377:
3373:
3368:
3366:
3362:
3358:
3357:
3351:
3347:
3343:
3339:
3329:
3322:
3320:
3318:
3314:
3310:
3306:
3298:
3296:
3292:
3282:
3276:
3272:
3268:
3263:
3254:
3245:
3241:
3230:
3226:
3222:
3217:
3213:
3209:
3205:
3201:
3197:
3193:
3192:
3191:
3179:
3170:
3162:
3158:
3153:
3149:
3146: −
3145:
3141:
3136:
3133: −
3132:
3128:
3123:
3119:
3115:
3111:
3107:
3103:
3099:
3095:
3091:
3085:
3081:
3077:
3072:
3068:
3064:
3060:
3056:
3050:
3046:
3042:
3037:
3033:
3029:
3025:
3021:
3017:
3013:
3009:
3005:
3001:
2997:
2993:
2989:
2988:
2987:
2983:
2978:
2974:
2970:
2966:
2962:
2957:
2951:
2943:
2931:
2925:
2919:
2916:
2910:
2907:
2901:
2895:
2892:
2889:
2883:
2880:
2877:
2869:
2866:
2860:
2854:
2851:
2848:
2842:
2839:
2833:
2830:
2827:
2824:
2821:
2813:
2807:
2801:
2795:
2789:
2786:
2780:
2774:
2768:
2765:
2759:
2756:
2753:
2745:
2739:
2733:
2727:
2724:
2718:
2712:
2706:
2700:
2694:
2691:
2685:
2682:
2678:
2661:
2659:
2642:
2640:
2623:
2621:
2604:
2602:
2585:
2583:
2566:
2564:
2547:
2545:
2528:
2526:
2509:
2507:
2490:
2488:
2471:
2469:
2452:
2449:
2445:
2440:
2439:
2438:
2372:
2369:
2365:
2313:
2293:
2279:
2274:
2269:
2264:
2259:
2256:
2246:
2238:
2230:
2227:
2224:
2221:
2211:
2203:
2195:
2187:
2179:
2176:
2160:
2146:
2135:
2124:
2116:
2113:
2097:
2086:
2075:
2064:
2056:
2053:
2048:
2042:
2037:
2032:
2027:
2022:
2019:
2014:
2011:
2008:
2005:
2002:
1999:
1994:
1991:
1988:
1985:
1982:
1979:
1969:
1961:
1958:
1955:
1952:
1949:
1939:
1931:
1928:
1925:
1922:
1919:
1915:
1910:
1909:
1906:
1905:
1897:
1894:
1891:
1888:
1885:
1882:
1879:
1876:
1873:
1870:
1865:
1862:
1859:
1856:
1853:
1850:
1847:
1844:
1841:
1838:
1828:
1820:
1812:
1804:
1796:
1788:
1780:
1772:
1764:
1761:
1756:
1753:
1750:
1747:
1744:
1741:
1738:
1735:
1732:
1729:
1724:
1720:
1717:
1714:
1711:
1708:
1705:
1702:
1699:
1696:
1693:
1688:
1685:
1682:
1679:
1676:
1673:
1670:
1667:
1664:
1661:
1651:
1643:
1640:
1637:
1634:
1631:
1628:
1625:
1622:
1619:
1614:
1611:
1608:
1605:
1602:
1599:
1596:
1593:
1590:
1587:
1582:
1578:
1575:
1572:
1569:
1566:
1563:
1560:
1557:
1554:
1551:
1546:
1543:
1540:
1537:
1534:
1531:
1528:
1525:
1522:
1519:
1509:
1506:
1503:
1500:
1497:
1494:
1491:
1488:
1485:
1482:
1477:
1474:
1471:
1468:
1465:
1462:
1459:
1456:
1453:
1450:
1446:
1441:
1440:
1429:
1421:
1413:
1405:
1397:
1389:
1381:
1378:
1375:
1373:
1370:
1369:
1360:
1352:
1344:
1336:
1328:
1320:
1317:
1314:
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1280:
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759:
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626:Alphasyllabic
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294:
293:
290:
287:
286:
282:
279:
278:
275:
272:
271:
267:
264:
263:
259:Other systems
255:
254:
247:
244:
242:
241:Counting rods
239:
238:
234:
233:
229:
226:
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221:
219:
216:
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211:
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204:
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4271:Intersection
4018:
3917:. Retrieved
3893:
3887:
3881:"Third base"
3877:Hayes, Brian
3856:. Retrieved
3846:
3822:
3815:
3800:
3785:
3736:
3730:
3705:
3699:
3693:
3666:
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3647:
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3609:
3598:. Retrieved
3588:
3577:. Retrieved
3573:
3563:
3546:
3509:
3501:
3496:such as the
3491:
3470:
3450:
3445:
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2971:) with base
2968:
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2816:000100111011
2662:
2643:
2624:
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932:
927:
845:
811:
809:
793:
789:
785:
780:, a ternary
765:
761:
726:
724:
492:
453:Signed-digit
372:
328:Contemporary
195:Contemporary
18:
4501:Type theory
4496:Type system
4346:Bottom type
4293:Option type
4234:generalized
4120:Long double
4065:Fixed point
3548:Taixuanjing
3313:hexadecimal
805:information
631:Akṣarapallī
601:Tally marks
500:Non-integer
4521:Categories
4406:Empty type
4401:Type class
4351:Collection
4308:Refinement
4286:metaobject
4134:signedness
3993:Data types
3919:2020-04-12
3858:2010-01-20
3641:(2): 9–12.
3600:2020-07-30
3579:2020-07-30
3555:References
3500:defined a
3451:A form of
3433:quaternary
3417:Cantor set
2863:0313452421
2804:0001011101
2421:, decimal
916:A ternary
668:Glagolitic
641:Kaṭapayādi
609:Alphabetic
513:Asymmetric
355:radix/base
296:Cistercian
281:Babylonian
228:Vietnamese
83:Devanagari
4481:Subtyping
4476:Interface
4459:metaclass
4411:Unit type
4381:Semaphore
4361:Exception
4266:Inductive
4256:Dependent
4221:Composite
4199:Character
4181:Reference
4078:Minifloat
4034:Bit array
3771:cite book
3671:CiteSeerX
3365:impedance
2450:Fraction
2389:, senary
2366:is not a
2330:(nor for
810:Although
636:Āryabhaṭa
581:Kharosthi
473:factorial
440:Bijective
341:(Iñupiaq)
171:Sundanese
166:Mongolian
113:Malayalam
4506:Variable
4396:Top type
4261:Equality
4169:physical
4146:Rational
4141:Interval
4088:bfloat16
3937:Archived
3910:Archived
3898:Sigma Xi
3828:Springer
3722:38704739
3522:See also
3510:de facto
3376:pitchers
3372:baseball
3350:grounded
2878:Decimal
2683:Ternary
2222:Decimal
2054:Ternary
2000:Decimal
1920:Ternary
1871:Decimal
1730:Ternary
1694:Decimal
1588:Ternary
1552:Decimal
1451:Ternary
792:nary dig
663:Georgian
653:Cyrillic
621:Armenian
576:Etruscan
571:Egyptian
479:Negative
339:Kaktovik
334:Cherokee
311:Pentadic
235:Historic
218:Japanese
151:Javanese
141:Balinese
128:Dzongkha
93:Gurmukhi
88:Gujarati
26:a series
24:Part of
4449:Generic
4425:Related
4341:Boolean
4298:Product
4174:virtual
4164:Address
4156:Pointer
4129:Integer
4060:Decimal
4055:Complex
4043:Numeric
3763:9603084
3461:carries
3415:or the
3403:⁄
3361:voltage
3332:useful)
3258:
3235:
3183:
3165:
3018:+ … + (
2822:Senary
2754:Binary
2676:
2664:
2657:
2645:
2638:
2626:
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2607:
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2569:
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2486:
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2375:
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2328:
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2308:
2296:
2290:As for
2177:Senary
2114:Binary
1980:Senary
1950:Binary
1839:Senary
1762:Binary
1662:Senary
1620:Binary
1520:Senary
1483:Binary
906:decimal
856:decimal
812:ternary
772:as its
766:trinary
727:ternary
566:Chuvash
484:Complex
274:Ancient
266:History
213:Hokkien
201:Chinese
146:Burmese
136:Tibetan
123:Kannada
103:Sinhala
78:Bengali
4439:Boxing
4427:topics
4386:Stream
4323:tagged
4281:Object
4204:String
3834:
3761:
3751:
3720:
3673:
3528:Qutrit
3513:binary
3482:C code
3429:binary
3317:binary
3112:+ … +
3065:+ … +
2934:076923
2908:0.125
2904:142857
2792:000111
2715:010212
2371:factor
2257:Power
2020:Power
890:(nine
866:senary
852:binary
822:, and
768:) has
762:base 3
678:Hebrew
648:Coptic
561:Brahmi
546:Aegean
503:
487:
469:
456:
443:
306:Muisca
246:Tangut
223:Korean
206:Suzhou
118:Telugu
4334:Other
4318:Union
4251:Class
4241:Array
4024:Tryte
3913:(PDF)
3896:(6).
3884:(PDF)
3759:S2CID
3718:S2CID
3657:(PDF)
3533:Setun
3502:tryte
3498:Setun
3492:Some
3488:Tryte
3446:trees
3354:high-
3344:with
3309:octal
3206:) = (
3190:Then
3069:+ 1),
3002:) = (
2849:0.043
2787:0.001
2736:00211
2368:prime
1641:1111
784:is a
782:digit
770:three
673:Greek
658:Geʽez
616:Abjad
596:Roman
556:Aztec
551:Attic
466:Mixed
424:table
316:Quipu
301:Mayan
156:Khmer
108:Tamil
4454:Kind
4416:Void
4276:List
4191:Text
4029:Word
4019:Trit
4014:Byte
3832:ISBN
3777:link
3749:ISBN
3706:C-24
3535:, a
3516:byte
3506:bits
3431:and
3380:outs
3338:CMOS
3311:and
3156:, or
3139:, so
2975:and
2926:0.08
2890:0.25
2867:0.03
2852:0.04
2831:0.13
2808:0.00
2798:0011
2771:0011
2766:0.01
2730:0022
2725:0.01
2703:0121
2170:0011
2167:1110
2164:1100
2156:0001
2153:1010
2150:1001
2142:1011
2139:1000
2137:1000
2131:1001
2128:1101
2120:0011
2118:1111
1995:213
1973:0001
1965:1011
1959:1001
1832:1010
1824:1001
1816:1000
1808:0111
1800:0110
1792:0101
1784:0100
1776:0011
1768:0010
1757:222
1655:0001
1647:0000
1638:1110
1635:1101
1632:1100
1629:1011
1626:1010
1623:1001
1615:122
1037:200
1003:100
892:bits
884:1101
881:0110
862:(10)
786:trit
774:base
321:Rumi
176:Thai
98:Odia
4313:Set
4009:Bit
3902:doi
3741:doi
3710:doi
3681:doi
3518:).
3392:3.2
3129:= −
3121:and
3088:= (
3053:= (
3026:+ (
3010:+ (
2917:0.1
2896:0.1
2893:0.2
2881:0.5
2855:0.0
2840:0.1
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2825:0.3
2796:0.0
2783:001
2775:0.0
2757:0.1
2748:002
2740:0.0
2707:0.0
2692:0.1
2437:).
2250:683
2242:561
2234:187
2228:729
2225:243
2215:043
2213:231
2207:213
2199:043
2191:213
2183:043
2162:100
2107:000
2104:000
2101:000
2093:000
2090:000
2088:100
2082:000
2079:000
2071:000
2068:000
2060:000
2058:100
2015:81
1971:101
1943:000
1935:000
1929:100
1898:26
1866:42
1754:221
1751:220
1748:212
1745:211
1742:210
1739:202
1736:201
1733:200
1721:17
1689:25
1612:121
1609:120
1606:112
1603:111
1600:110
1597:102
1594:101
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1547:12
1513:000
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1498:100
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1425:200
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1401:200
1393:100
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1376:100
1372:100
1364:200
1356:101
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1340:210
1332:111
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1192:110
1177:200
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864:or
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790:tri
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3273:,
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3227:,
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3150:=
3144:bM
3116:+
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1992:43
1989:13
1956:11
1941:10
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1886:22
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1880:20
1877:19
1874:18
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1718:16
1715:15
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1709:13
1706:12
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1700:10
1686:24
1683:23
1680:22
1677:21
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1671:15
1668:14
1665:13
1579:8
1544:11
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1495:11
1492:10
1475:21
1472:20
1469:12
1466:11
1463:10
1431:10
1312:22
1308:22
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1244:21
1189:20
1185:20
1135:12
1131:12
1089:22
1086:11
1082:11
1050:20
1047:10
1043:10
1022:22
1019:20
1016:11
1000:22
997:21
994:20
991:12
988:11
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3275:d
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3267:N
3260:,
3253:b
3249:/
3244:b
3240:b
3238:(
3231:)
3229:d
3225:b
3223:(
3221:N
3214:,
3212:M
3208:b
3204:d
3200:b
3198:(
3196:N
3185:.
3178:b
3174:/
3169:b
3161:M
3152:b
3148:M
3135:b
3131:b
3127:M
3125:−
3118:b
3114:b
3110:b
3106:b
3097:.
3094:M
3090:b
3086:)
3084:d
3080:b
3078:(
3076:N
3067:b
3063:b
3059:b
3055:b
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3049:d
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3041:N
3034:,
3032:b
3028:b
3024:b
3020:b
3016:b
3012:b
3008:b
3004:b
3000:d
2996:b
2994:(
2992:N
2982:b
2977:d
2973:b
2969:d
2965:b
2963:(
2961:N
2950:n
2928:3
2913:1
2898:6
2886:3
2857:3
2836:1
2709:1
2688:1
2670:/
2667:1
2651:/
2648:1
2632:/
2629:1
2613:/
2610:1
2597:9
2594:/
2591:1
2578:8
2575:/
2572:1
2559:7
2556:/
2553:1
2540:6
2537:/
2534:1
2521:5
2518:/
2515:1
2502:4
2499:/
2496:1
2483:3
2480:/
2477:1
2464:2
2461:/
2458:1
2432:6
2429:/
2426:1
2413:/
2410:1
2397:/
2394:1
2381:/
2378:1
2364:2
2357:8
2354:/
2351:1
2341:4
2338:/
2335:1
2325:2
2322:/
2319:1
2305:3
2302:/
2299:1
2281:3
2276:3
2271:3
2266:3
2261:3
2240:6
2232:2
2189:3
2181:1
2148:1
2099:1
2066:1
2044:3
2039:3
2034:3
2029:3
2024:3
2009:9
2006:3
2003:1
1986:3
1983:1
1963:1
1953:1
1933:1
1923:1
1830:1
1822:1
1814:1
1806:1
1798:1
1790:1
1782:1
1774:1
1766:1
1697:9
1653:1
1645:1
1576:7
1573:6
1570:5
1567:4
1564:3
1561:2
1558:1
1555:0
1538:5
1535:4
1532:3
1529:2
1526:1
1523:0
1511:1
1489:1
1486:0
1460:2
1457:1
1454:0
1423:2
1415:2
1407:2
1399:1
1391:1
1383:1
1362:2
1354:2
1346:2
1338:1
1330:1
1322:1
1298:2
1290:2
1282:1
1274:1
1266:1
1258:1
1234:2
1226:1
1218:1
1210:1
1202:1
1175:1
1167:1
1159:1
1151:1
1121:1
1113:1
1105:1
1072:1
1013:2
1009:2
982:2
979:1
975:1
933:2
928:1
924:×
879:1
869:1
824:2
820:1
816:0
800:2
788:(
753:/
750:i
744:n
738:t
735:ˈ
732:/
714:e
707:t
700:v
509:)
507:φ
505:(
496:)
493:i
491:2
489:(
475:)
471:(
462:)
458:(
449:)
447:1
445:(
426:)
422:(
393:8
388:6
383:5
378:4
373:3
368:2
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