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Superincreasing sequence

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Sum: 0 Element: 1 Sum: 1 Element: 3 Sum: 4 Element: 6 Sum: 10 Element: 13 Sum: 23 Element: 27 Sum: 50 Element: 52 Superincreasing sequence? True
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if every element of the sequence is greater than the sum of all previous elements in the sequence.
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Multiplying a superincreasing sequence by a positive real constant keeps it superincreasing.
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source code tests a sequence of numbers to determine if it is superincreasing:
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An Introduction to Cryptography (Discrete Mathematical & Applications)
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Applied Cryptography: Protocols, Algorithms, and Source Code in C
395:, pages 463-464, Wiley; 2nd edition (October 18, 1996), 425: 372:, Chapman & Hall/CRC; 1 edition (August 10, 2000), 101: 33: 154: 77: 155:{\displaystyle s_{n+1}>\sum _{j=1}^{n}s_{j}} 445: 8: 92:Formally, this condition can be written as 452: 438: 387: 385: 146: 136: 125: 106: 100: 54: 41: 32: 420:This cryptography-related article is a 361: 297:"Superincreasing sequence? " 7: 410: 408: 351:Merkleā€“Hellman knapsack cryptosystem 311:This produces the following output: 327:, but (1, 3, 4, 9, 15, 25) is not. 14: 78:{\displaystyle (s_{1},s_{2},...)} 412: 72: 34: 1: 424:. You can help Knowledge by 323:(1, 3, 6, 13, 27, 52) is a 492: 407: 330:The series a^x for a>=2 325:superincreasing sequence 183: 156: 141: 79: 243:"Element: " 157: 121: 80: 99: 31: 368:Richard A. Mollin, 476:Cryptography stubs 152: 75: 433: 432: 231:"Sum: " 483: 454: 447: 440: 416: 409: 403: 391:Bruce Schneier, 389: 380: 366: 307: 304: 301: 298: 295: 292: 289: 286: 283: 280: 277: 274: 271: 268: 265: 262: 259: 256: 253: 250: 247: 244: 241: 238: 235: 232: 229: 226: 223: 220: 217: 214: 211: 208: 205: 202: 199: 196: 193: 190: 187: 161: 159: 158: 153: 151: 150: 140: 135: 117: 116: 84: 82: 81: 76: 59: 58: 46: 45: 491: 490: 486: 485: 484: 482: 481: 480: 461: 460: 459: 458: 406: 390: 383: 367: 363: 359: 347: 337: 320: 315: 309: 308: 305: 302: 299: 296: 293: 290: 287: 284: 281: 278: 275: 272: 269: 266: 263: 260: 257: 254: 251: 248: 245: 242: 239: 236: 233: 230: 227: 224: 221: 218: 215: 212: 209: 206: 203: 200: 197: 194: 191: 188: 185: 175: 142: 102: 97: 96: 87:superincreasing 50: 37: 29: 28: 12: 11: 5: 489: 487: 479: 478: 473: 463: 462: 457: 456: 449: 442: 434: 431: 430: 417: 405: 404: 381: 360: 358: 355: 354: 353: 346: 343: 342: 341: 336: 333: 332: 331: 328: 319: 316: 313: 184: 177:The following 174: 171: 163: 162: 149: 145: 139: 134: 131: 128: 124: 120: 115: 112: 109: 105: 74: 71: 68: 65: 62: 57: 53: 49: 44: 40: 36: 13: 10: 9: 6: 4: 3: 2: 488: 477: 474: 472: 469: 468: 466: 455: 450: 448: 443: 441: 436: 435: 429: 427: 423: 418: 415: 411: 402: 401:0-471-11709-9 398: 394: 388: 386: 382: 379: 378:1-58488-127-5 375: 371: 365: 362: 356: 352: 349: 348: 344: 339: 338: 334: 329: 326: 322: 321: 317: 312: 182: 180: 172: 170: 168: 147: 143: 137: 132: 129: 126: 122: 118: 113: 110: 107: 103: 95: 94: 93: 90: 88: 69: 66: 63: 60: 55: 51: 47: 42: 38: 27: 23: 19: 471:Cryptography 426:expanding it 419: 392: 369: 364: 324: 310: 176: 166: 164: 91: 86: 26:real numbers 24:of positive 15: 18:mathematics 465:Categories 357:References 335:Properties 85:is called 123:∑ 345:See also 318:Examples 219:sequence 186:sequence 165:for all 22:sequence 173:Program 399:  376:  179:Python 291:print 282:total 279:break 276:False 264:total 261:<= 237:total 225:print 192:total 169:ā‰„ 1. 422:stub 397:ISBN 374:ISBN 303:test 270:test 207:True 201:test 119:> 20:, a 210:for 16:In 467:: 384:^ 285:+= 255:if 216:in 453:e 446:t 439:v 428:. 306:) 300:, 294:( 288:n 273:= 267:: 258:n 252:) 249:n 246:, 240:, 234:, 228:( 222:: 213:n 204:= 198:0 195:= 189:= 167:n 148:j 144:s 138:n 133:1 130:= 127:j 114:1 111:+ 108:n 104:s 73:) 70:. 67:. 64:. 61:, 56:2 52:s 48:, 43:1 39:s 35:(

Index

mathematics
sequence
real numbers
Python
Merkleā€“Hellman knapsack cryptosystem
ISBN
1-58488-127-5


ISBN
0-471-11709-9
Stub icon
stub
expanding it
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t
e
Categories
Cryptography
Cryptography stubs

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