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hexagonal numbers
A figurate number of form n(2n-1). more

The first 600 hexagonal numbers :
1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276, 325, 378, 435, 496, 561, 630, 703, 780, 861, 946, 1035, 1128, 1225, 1326, 1431, 1540, 1653, 1770, 1891, 2016, 2145, 2278, 2415, 2556, 2701, 2850, 3003, 3160, 3321, 3486, 3655, 3828, 4005, 4186, 4371, 4560, 4753, 4950, 5151, 5356, 5565, 5778, 5995, 6216, 6441, 6670, 6903, 7140, 7381, 7626, 7875, 8128, 8385, 8646, 8911, 9180, 9453, 9730, 10011, 10296, 10585, 10878, 11175, 11476, 11781, 12090, 12403, 12720, 13041, 13366, 13695, 14028, 14365, 14706, 15051, 15400, 15753, 16110, 16471, 16836, 17205, 17578, 17955, 18336, 18721, 19110, 19503, 19900, 20301, 20706, 21115, 21528, 21945, 22366, 22791, 23220, 23653, 24090, 24531, 24976, 25425, 25878, 26335, 26796, 27261, 27730, 28203, 28680, 29161, 29646, 30135, 30628, 31125, 31626, 32131, 32640, 33153, 33670, 34191, 34716, 35245, 35778, 36315, 36856, 37401, 37950, 38503, 39060, 39621, 40186, 40755, 41328, 41905, 42486, 43071, 43660, 44253, 44850, 45451, 46056, 46665, 47278, 47895, 48516, 49141, 49770, 50403, 51040, 51681, 52326, 52975, 53628, 54285, 54946, 55611, 56280, 56953, 57630, 58311, 58996, 59685, 60378, 61075, 61776, 62481, 63190, 63903, 64620, 65341, 66066, 66795, 67528, 68265, 69006, 69751, 70500, 71253, 72010, 72771, 73536, 74305, 75078, 75855, 76636, 77421, 78210, 79003, 79800, 80601, 81406, 82215, 83028, 83845, 84666, 85491, 86320, 87153, 87990, 88831, 89676, 90525, 91378, 92235, 93096, 93961, 94830, 95703, 96580, 97461, 98346, 99235, 100128, 101025, 101926, 102831, 103740, 104653, 105570, 106491, 107416, 108345, 109278, 110215, 111156, 112101, 113050, 114003, 114960, 115921, 116886, 117855, 118828, 119805, 120786, 121771, 122760, 123753, 124750, 125751, 126756, 127765, 128778, 129795, 130816, 131841, 132870, 133903, 134940, 135981, 137026, 138075, 139128, 140185, 141246, 142311, 143380, 144453, 145530, 146611, 147696, 148785, 149878, 150975, 152076, 153181, 154290, 155403, 156520, 157641, 158766, 159895, 161028, 162165, 163306, 164451, 165600, 166753, 167910, 169071, 170236, 171405, 172578, 173755, 174936, 176121, 177310, 178503, 179700, 180901, 182106, 183315, 184528, 185745, 186966, 188191, 189420, 190653, 191890, 193131, 194376, 195625, 196878, 198135, 199396, 200661, 201930, 203203, 204480, 205761, 207046, 208335, 209628, 210925, 212226, 213531, 214840, 216153, 217470, 218791, 220116, 221445, 222778, 224115, 225456, 226801, 228150, 229503, 230860, 232221, 233586, 234955, 236328, 237705, 239086, 240471, 241860, 243253, 244650, 246051, 247456, 248865, 250278, 251695, 253116, 254541, 255970, 257403, 258840, 260281, 261726, 263175, 264628, 266085, 267546, 269011, 270480, 271953, 273430, 274911, 276396, 277885, 279378, 280875, 282376, 283881, 285390, 286903, 288420, 289941, 291466, 292995, 294528, 296065, 297606, 299151, 300700, 302253, 303810, 305371, 306936, 308505, 310078, 311655, 313236, 314821, 316410, 318003, 319600, 321201, 322806, 324415, 326028, 327645, 329266, 330891, 332520, 334153, 335790, 337431, 339076, 340725, 342378, 344035, 345696, 347361, 349030, 350703, 352380, 354061, 355746, 357435, 359128, 360825, 362526, 364231, 365940, 367653, 369370, 371091, 372816, 374545, 376278, 378015, 379756, 381501, 383250, 385003, 386760, 388521, 390286, 392055, 393828, 395605, 397386, 399171, 400960, 402753, 404550, 406351, 408156, 409965, 411778, 413595, 415416, 417241, 419070, 420903, 422740, 424581, 426426, 428275, 430128, 431985, 433846, 435711, 437580, 439453, 441330, 443211, 445096, 446985, 448878, 450775, 452676, 454581, 456490, 458403, 460320, 462241, 464166, 466095, 468028, 469965, 471906, 473851, 475800, 477753, 479710, 481671, 483636, 485605, 487578, 489555, 491536, 493521, 495510, 497503, 499500, 501501, 503506, 505515, 507528, 509545, 511566, 513591, 515620, 517653, 519690, 521731, 523776, 525825, 527878, 529935, 531996, 534061, 536130, 538203, 540280, 542361, 544446, 546535, 548628, 550725, 552826, 554931, 557040, 559153, 561270, 563391, 565516, 567645, 569778, 571915, 574056, 576201, 578350, 580503, 582660, 584821, 586986, 589155, 591328, 593505, 595686, 597871, 600060, 602253, 604450, 606651, 608856, 611065, 613278, 615495, 617716, 619941, 622170, 624403, 626640, 628881, 631126, 633375, 635628, 637885, 640146, 642411, 644680, 646953, 649230, 651511, 653796, 656085, 658378, 660675, 662976, 665281, 667590, 669903, 672220, 674541, 676866, 679195, 681528, 683865, 686206, 688551, 690900, 693253, 695610, 697971, 700336, 702705, 705078, 707455, 709836, 712221, 714610, 717003, 719400.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 22360680 values, from 1 to 999999997764120).

n\r 0  1 
21118034011180340 2 
31490712074535600 3 
45590170559017055901705590170 4 
589442728944272044721360 5 
6745356037267800745356037267800 6 
76388765638876606388766003194383 7 
827950852795085279508527950852795085279508527950852795085 8 
9496904074535600496904000496904000 9 
104472136447213602236068044721364472136022360680 10 
1140655784065579040655782032789040655780004065578

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.