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10, and Ɛ represents 11. It's nice to know that specific symbols exists for base 12, but it seems to me that it might be confusing to use them in one case (base 12), and use letters for any other base greater than 10 in the same page. 'Ɛ' has previously been removed by anonymous with no explanation, probably because it seemed out of place, and then put back by Arthur Rubin without a real explanation. I don't want to revert back my change without first asking other editors what they think. Please comment.
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and therefore arduous indeed before the advent of calculators. My method requires manual long division of an extendible dividend by a fixed integer. All of the published dates that I have found associated with "parasite numbers" are in the late 20th and early 21st century; my original solution (the first Reaman
Numeral with its "do-si-do digit" of 9) dates back to 1953, as described in the "Historical Note" at
22:
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18,27,36,45,54,63,72,81,90. On one case it adds up to ten and on the other it adds up to nine. To see such proof you must divide 1 by 81 and multiply the answer beginning with one to 9 and see the pattern that takes place. A sequence for example reveals such description by dividing 1 by 999991 to 1 divided by 999999. Cyclic or permutable numbers are another examples.
689:: "All cyclic numbers are divisible by 'base−1' (9 in decimal) and the sum of the remainder is the a multiple of the divisor. (This follows from the previous point.)" In addition to it containing an obvious grammatical error... what exactly does it mean? Specifically, the sum of what remainder is a multiple of what divisor?
722:
I recently "fixed" line 70, where I replaced the 'Ɛ' in this number '076Ɛ45076Ɛ45076Ɛ45' by a 'B', because when using a base greater than 10, it is common practice to use letters A through Z... However, I am now just finding out that there is a notation specifically for duodecimal where ᘔ represents
378:
Following up on your most recent entry here: I have studied parasite numbers as you suggested and, yes, "parasite numbers" do indeed map to "Reaman
Numerals" but with an entirely different derivation -- a derivation that requires division by extraordinarily long decimal representation of a fraction
805:
It says that "if the digital period of 1/p (where p is prime) is p − 1, then the digits represent a cyclic number". This is incorrect. It is only if p is a maximal prime number, i.e. 7,17,19, 23, 29, 47... For all other prime numbers, the period is not cyclic as defined in the previous section
415:
Taking the last digits of the multiplication table combining them with the digits that sum up to 10 give a direct and an opposite direction. For example given a number 10 and adding nine to it,it gives 19,28,37,46,55,64,73,82,91, and if it was multiples of nine the answer would be
269:
Now, I am not a mathematician. What I want to know is surely obvious: Have numbers with this property been discovered by others? If so, what are they called? If not, I would be delighted if wikipedia were to give recognition to Reaman
Numerals, including links as given above.
315:
A081463 Numbers which when multiplied by their final digit have products with same digital sequence except that last is first. Numbers obtained by concatenating a term any number of times with itself also have the defining property and are
351:
It's good that you suggested to someone else to add it as opposed to adding it yourself. The most important thing to avoid here is the appearance of linkspam. I will carefully look over your site and I will also put the question to the
257:
In 1953, I (independently) discovered what I called a "Reaman
Numeral" (after my father's first name). As you will see, it has 44 digits: 10,112,359,550,561,797,752,808,988,764,044,943,820,224,719. Its derivation is available at
341:
Thanks for the information. I will chase down the provenance for dates and add an epilog preceded by "also known as 'parasitic numbers'..." on the solution page. Now, what are your thoughts about an
External link to my site?
395:
A year and a half later, my great-grandchildren and I are still waiting for a reply to my previous follow-up, hoping with ego at the ready for a favorable verdict and thus recognition of my little 1953 discovery.
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Please accept my gratitude for your diligence in addressing my suggestion. I shall be glad to receive any guidance you and others might care to make. Best wishes for 2007 -- and beyond.
779:
multiple of the divisor" (my emphasis) I'd have thought that the remainder was always less than the divisor, but in any event it can't be both the and a, can it?
495:
Interesting question to know why numbers share between themselves and how they share. When they are given a space between themselves they don't share. example
383:. My great-grandchildren and I await your judgment on whether an external link would add value to the "parasite numbers" article (or some other) in Knowledge.
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I would prefer "Reaman" to "parasitic," but it might be too late to do anything about it. Back in 1953 you might have been able to change the tide.
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I traslated article in russian and I think also, that sentence is not clear. I have to remove it from translation to russian.
806:'Details'. In fact, this section explicitly mentions the number 076923, which is the period of 1/13, as not being cyclic.
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Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
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Also, the article isn't clear on how long of a run it required to call it a cyclic number - does it have to generate
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With
Babylonian mathematics you'll be dealing with 60 and 59 and with our base ten digits it would be ten and nine.
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I think they might be called "parasitic numbers." Remove the commas and enter the numeral into the
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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One divided by 81=0.012345679..... a cyclic number with 10,19,28,37,46,55,64,73,1 as remainders
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748:(all successive multiples being cyclic permutations) listed in the Special Cases section above)
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which gives you hint on the period of the repeating decimal once you know the denominator.--
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Re 5 & repeated digits - this should be thrown out. Or do I miss something? --
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Difference from 16 to 7 of the remainders always nine on a cyclic # except 1/7.
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Repeated quotient:0588235294117647. If from 0 to 5 of the quotient is positive
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I have tried others base math, the only similarities I've found is with
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270+396=666,216+450=666,306+360=666,378+288=666,36+630=666,162+504=666,
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Adding the first eight remainders to the second half, always equals 17.
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Multiplying each remainder by the quotient gives a cyclic number.
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Main article and sub-article relationship has been established.--
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Yes and the period of 1/13 is 6, not 12 (which is 13 - 1). --
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and the sum of the remainder is the a multiple of the divisor.
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permutations in order to be considered cyclic? Or just some?
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Only works when the quotient has a length of an even number.
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16 repeated remainders:10,15,14,4,6,9,5,16,7,2,3,13,11,8,12,1
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remainders= 270,216,306,378,36,162,396,450,360,288,630,504
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Have you tried looking at this in bases other than base 10?
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I'm not sure I understand "and the sum of the remainder is
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Unclear point in the section "Properties of cyclic numbers"
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1/666=5, 24, 19, 27, 34, 3, 14, 35, 40, 32, 25, 56, 45
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24+35=59,19+40=59,27+32=59,34+25=59,3+56=59,14+45=59,
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No, they haven't, and there's no reason to merge. —
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The following trivial cases are typically excluded:
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Subsequent comments should be made in a new section.
101:, a collaborative effort to improve the coverage of
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Representation of digits in base 12 and other bases
356:project members. In the meantime, merry Christmas!
647:But those aren't cyclic numbers anyway, are they?
685:The following sentence currently appears under
178:A summary of the conclusions reached follows.
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455:1/17=0.058823529411764705882352941176470....
381:http://www.niquette.com/puzzles/reaman1s.htm
801:Cyclic numbers and digital period of primes
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264:http://niquette.com/puzzles/reaman2p.htm
260:http://niquette.com/puzzles/reaman1p.htm
691:2A02:8109:9340:136C:309A:2996:B95D:ACF7
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627:Trivial cases? And more info requested
485:0588235294117647*136=79999999999999992
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169:The following discussion is closed.
95:This article is within the scope of
262:, and other Reamans are derived at
158:Suggest to merge this article with
38:It is of interest to the following
505:1/9991=0.000100090081072965669....
325:A092697 Least n-parasitic number.
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851:Low-priority mathematics articles
115:Knowledge:WikiProject Mathematics
308:search box. Two results come up:
244:The discussion above is closed.
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470:then from 9 to 4 is negative 5.
135:This article has been rated as
622:16:28, 23 September 2009 (UTC)
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225:13:46, 10 September 2009 (UTC)
210:12:47, 30 September 2008 (UTC)
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604:Cyclic permutation of integer
584:Cyclic permutation of integer
578:Cyclic permutation of integer
479:The sum of the remainders:136
370:13:53, 22 December 2006 (UTC)
361:20:51, 21 December 2006 (UTC)
347:04:04, 21 December 2006 (UTC)
337:22:11, 20 December 2006 (UTC)
275:23:59, 19 December 2006 (UTC)
192:16:42, 12 February 2013 (UTC)
109:and see a list of open tasks.
846:C-Class mathematics articles
831:19:57, 17 October 2023 (UTC)
816:07:20, 17 October 2023 (UTC)
687:Properties of cyclic numbers
573:22:23, 29 January 2008 (UTC)
560:sum of remainders 666*6=3996
451:example of a cyclic number.
447:12345679*9= 1 1 1 1 1 1 1 1
444:12345679*8= 9 8 7 6 5 4 3 2
441:12345679*7= 8 6 4 1 9 7 5 3
438:12345679*6= 7 4 0 7 4 0 7 4
435:12345679*5= 6 1 7 2 8 3 9 5
432:12345679*4= 4 9 3 8 2 7 1 6
429:12345679*3= 3 7 0 3 7 0 3 7
426:12345679*2= 2 4 6 9 1 3 5 8
423:12345679*1= 1 2 3 4 5 6 7 9
388:00:29, 8 January 2007 (UTC)
282:Paul, you may now refer to
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641:repeated digits, e.g.: 555
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554:sum of quotients 59*6=354
509:21:24, May 24, 2007 user
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246:Please do not modify it.
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602:Actually, I think
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