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pentagonal numbers
A figurate number of form n(3n-1)/2. more

The first 600 pentagonal numbers :
1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 210, 247, 287, 330, 376, 425, 477, 532, 590, 651, 715, 782, 852, 925, 1001, 1080, 1162, 1247, 1335, 1426, 1520, 1617, 1717, 1820, 1926, 2035, 2147, 2262, 2380, 2501, 2625, 2752, 2882, 3015, 3151, 3290, 3432, 3577, 3725, 3876, 4030, 4187, 4347, 4510, 4676, 4845, 5017, 5192, 5370, 5551, 5735, 5922, 6112, 6305, 6501, 6700, 6902, 7107, 7315, 7526, 7740, 7957, 8177, 8400, 8626, 8855, 9087, 9322, 9560, 9801, 10045, 10292, 10542, 10795, 11051, 11310, 11572, 11837, 12105, 12376, 12650, 12927, 13207, 13490, 13776, 14065, 14357, 14652, 14950, 15251, 15555, 15862, 16172, 16485, 16801, 17120, 17442, 17767, 18095, 18426, 18760, 19097, 19437, 19780, 20126, 20475, 20827, 21182, 21540, 21901, 22265, 22632, 23002, 23375, 23751, 24130, 24512, 24897, 25285, 25676, 26070, 26467, 26867, 27270, 27676, 28085, 28497, 28912, 29330, 29751, 30175, 30602, 31032, 31465, 31901, 32340, 32782, 33227, 33675, 34126, 34580, 35037, 35497, 35960, 36426, 36895, 37367, 37842, 38320, 38801, 39285, 39772, 40262, 40755, 41251, 41750, 42252, 42757, 43265, 43776, 44290, 44807, 45327, 45850, 46376, 46905, 47437, 47972, 48510, 49051, 49595, 50142, 50692, 51245, 51801, 52360, 52922, 53487, 54055, 54626, 55200, 55777, 56357, 56940, 57526, 58115, 58707, 59302, 59900, 60501, 61105, 61712, 62322, 62935, 63551, 64170, 64792, 65417, 66045, 66676, 67310, 67947, 68587, 69230, 69876, 70525, 71177, 71832, 72490, 73151, 73815, 74482, 75152, 75825, 76501, 77180, 77862, 78547, 79235, 79926, 80620, 81317, 82017, 82720, 83426, 84135, 84847, 85562, 86280, 87001, 87725, 88452, 89182, 89915, 90651, 91390, 92132, 92877, 93625, 94376, 95130, 95887, 96647, 97410, 98176, 98945, 99717, 100492, 101270, 102051, 102835, 103622, 104412, 105205, 106001, 106800, 107602, 108407, 109215, 110026, 110840, 111657, 112477, 113300, 114126, 114955, 115787, 116622, 117460, 118301, 119145, 119992, 120842, 121695, 122551, 123410, 124272, 125137, 126005, 126876, 127750, 128627, 129507, 130390, 131276, 132165, 133057, 133952, 134850, 135751, 136655, 137562, 138472, 139385, 140301, 141220, 142142, 143067, 143995, 144926, 145860, 146797, 147737, 148680, 149626, 150575, 151527, 152482, 153440, 154401, 155365, 156332, 157302, 158275, 159251, 160230, 161212, 162197, 163185, 164176, 165170, 166167, 167167, 168170, 169176, 170185, 171197, 172212, 173230, 174251, 175275, 176302, 177332, 178365, 179401, 180440, 181482, 182527, 183575, 184626, 185680, 186737, 187797, 188860, 189926, 190995, 192067, 193142, 194220, 195301, 196385, 197472, 198562, 199655, 200751, 201850, 202952, 204057, 205165, 206276, 207390, 208507, 209627, 210750, 211876, 213005, 214137, 215272, 216410, 217551, 218695, 219842, 220992, 222145, 223301, 224460, 225622, 226787, 227955, 229126, 230300, 231477, 232657, 233840, 235026, 236215, 237407, 238602, 239800, 241001, 242205, 243412, 244622, 245835, 247051, 248270, 249492, 250717, 251945, 253176, 254410, 255647, 256887, 258130, 259376, 260625, 261877, 263132, 264390, 265651, 266915, 268182, 269452, 270725, 272001, 273280, 274562, 275847, 277135, 278426, 279720, 281017, 282317, 283620, 284926, 286235, 287547, 288862, 290180, 291501, 292825, 294152, 295482, 296815, 298151, 299490, 300832, 302177, 303525, 304876, 306230, 307587, 308947, 310310, 311676, 313045, 314417, 315792, 317170, 318551, 319935, 321322, 322712, 324105, 325501, 326900, 328302, 329707, 331115, 332526, 333940, 335357, 336777, 338200, 339626, 341055, 342487, 343922, 345360, 346801, 348245, 349692, 351142, 352595, 354051, 355510, 356972, 358437, 359905, 361376, 362850, 364327, 365807, 367290, 368776, 370265, 371757, 373252, 374750, 376251, 377755, 379262, 380772, 382285, 383801, 385320, 386842, 388367, 389895, 391426, 392960, 394497, 396037, 397580, 399126, 400675, 402227, 403782, 405340, 406901, 408465, 410032, 411602, 413175, 414751, 416330, 417912, 419497, 421085, 422676, 424270, 425867, 427467, 429070, 430676, 432285, 433897, 435512, 437130, 438751, 440375, 442002, 443632, 445265, 446901, 448540, 450182, 451827, 453475, 455126, 456780, 458437, 460097, 461760, 463426, 465095, 466767, 468442, 470120, 471801, 473485, 475172, 476862, 478555, 480251, 481950, 483652, 485357, 487065, 488776, 490490, 492207, 493927, 495650, 497376, 499105, 500837, 502572, 504310, 506051, 507795, 509542, 511292, 513045, 514801, 516560, 518322, 520087, 521855, 523626, 525400, 527177, 528957, 530740, 532526, 534315, 536107, 537902, 539700.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 25819889 values, from 1 to 999999989048537).

n\r 0  1 
21290994412909945 2 
3860662986066308606630 3 
46454972645497364549726454972 4 
51032795551639781032795600 5 
6430331543033154303314430331443033154303316 6 
77377110737711236885550073771120 7 
832274863227487322748632274863227486322748632274863227486 8 
9286887628688772868876286887728688772868877286887628688762868877 9 
105163977258199051639790051639782581988516397700 10 
1146945254694526469452504694525234726304694525000

A pictorial representation of the table above
motab
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.