Figurate numbers of the form 7n(n-1)/2 + 1. more
The first 600 centered heptagonal numbers :
1,
8,
22,
43,
71,
106,
148,
197,
253,
316,
386,
463,
547,
638,
736,
841,
953,
1072,
1198,
1331,
1471,
1618,
1772,
1933,
2101,
2276,
2458,
2647,
2843,
3046,
3256,
3473,
3697,
3928,
4166,
4411,
4663,
4922,
5188,
5461,
5741,
6028,
6322,
6623,
6931,
7246,
7568,
7897,
8233,
8576,
8926,
9283,
9647,
10018,
10396,
10781,
11173,
11572,
11978,
12391,
12811,
13238,
13672,
14113,
14561,
15016,
15478,
15947,
16423,
16906,
17396,
17893,
18397,
18908,
19426,
19951,
20483,
21022,
21568,
22121,
22681,
23248,
23822,
24403,
24991,
25586,
26188,
26797,
27413,
28036,
28666,
29303,
29947,
30598,
31256,
31921,
32593,
33272,
33958,
34651,
35351,
36058,
36772,
37493,
38221,
38956,
39698,
40447,
41203,
41966,
42736,
43513,
44297,
45088,
45886,
46691,
47503,
48322,
49148,
49981,
50821,
51668,
52522,
53383,
54251,
55126,
56008,
56897,
57793,
58696,
59606,
60523,
61447,
62378,
63316,
64261,
65213,
66172,
67138,
68111,
69091,
70078,
71072,
72073,
73081,
74096,
75118,
76147,
77183,
78226,
79276,
80333,
81397,
82468,
83546,
84631,
85723,
86822,
87928,
89041,
90161,
91288,
92422,
93563,
94711,
95866,
97028,
98197,
99373,
100556,
101746,
102943,
104147,
105358,
106576,
107801,
109033,
110272,
111518,
112771,
114031,
115298,
116572,
117853,
119141,
120436,
121738,
123047,
124363,
125686,
127016,
128353,
129697,
131048,
132406,
133771,
135143,
136522,
137908,
139301,
140701,
142108,
143522,
144943,
146371,
147806,
149248,
150697,
152153,
153616,
155086,
156563,
158047,
159538,
161036,
162541,
164053,
165572,
167098,
168631,
170171,
171718,
173272,
174833,
176401,
177976,
179558,
181147,
182743,
184346,
185956,
187573,
189197,
190828,
192466,
194111,
195763,
197422,
199088,
200761,
202441,
204128,
205822,
207523,
209231,
210946,
212668,
214397,
216133,
217876,
219626,
221383,
223147,
224918,
226696,
228481,
230273,
232072,
233878,
235691,
237511,
239338,
241172,
243013,
244861,
246716,
248578,
250447,
252323,
254206,
256096,
257993,
259897,
261808,
263726,
265651,
267583,
269522,
271468,
273421,
275381,
277348,
279322,
281303,
283291,
285286,
287288,
289297,
291313,
293336,
295366,
297403,
299447,
301498,
303556,
305621,
307693,
309772,
311858,
313951,
316051,
318158,
320272,
322393,
324521,
326656,
328798,
330947,
333103,
335266,
337436,
339613,
341797,
343988,
346186,
348391,
350603,
352822,
355048,
357281,
359521,
361768,
364022,
366283,
368551,
370826,
373108,
375397,
377693,
379996,
382306,
384623,
386947,
389278,
391616,
393961,
396313,
398672,
401038,
403411,
405791,
408178,
410572,
412973,
415381,
417796,
420218,
422647,
425083,
427526,
429976,
432433,
434897,
437368,
439846,
442331,
444823,
447322,
449828,
452341,
454861,
457388,
459922,
462463,
465011,
467566,
470128,
472697,
475273,
477856,
480446,
483043,
485647,
488258,
490876,
493501,
496133,
498772,
501418,
504071,
506731,
509398,
512072,
514753,
517441,
520136,
522838,
525547,
528263,
530986,
533716,
536453,
539197,
541948,
544706,
547471,
550243,
553022,
555808,
558601,
561401,
564208,
567022,
569843,
572671,
575506,
578348,
581197,
584053,
586916,
589786,
592663,
595547,
598438,
601336,
604241,
607153,
610072,
612998,
615931,
618871,
621818,
624772,
627733,
630701,
633676,
636658,
639647,
642643,
645646,
648656,
651673,
654697,
657728,
660766,
663811,
666863,
669922,
672988,
676061,
679141,
682228,
685322,
688423,
691531,
694646,
697768,
700897,
704033,
707176,
710326,
713483,
716647,
719818,
722996,
726181,
729373,
732572,
735778,
738991,
742211,
745438,
748672,
751913,
755161,
758416,
761678,
764947,
768223,
771506,
774796,
778093,
781397,
784708,
788026,
791351,
794683,
798022,
801368,
804721,
808081,
811448,
814822,
818203,
821591,
824986,
828388,
831797,
835213,
838636,
842066,
845503,
848947,
852398,
855856,
859321,
862793,
866272,
869758,
873251,
876751,
880258,
883772,
887293,
890821,
894356,
897898,
901447,
905003,
908566,
912136,
915713,
919297,
922888,
926486,
930091,
933703,
937322,
940948,
944581,
948221,
951868,
955522,
959183,
962851,
966526,
970208,
973897,
977593,
981296,
985006,
988723,
992447,
996178,
999916,
1003661,
1007413,
1011172,
1014938,
1018711,
1022491,
1026278,
1030072,
1033873,
1037681,
1041496,
1045318,
1049147,
1052983,
1056826,
1060676,
1064533,
1068397,
1072268,
1076146,
1080031,
1083923,
1087822,
1091728,
1095641,
1099561,
1103488,
1107422,
1111363,
1115311,
1119266,
1123228,
1127197,
1131173,
1135156,
1139146,
1143143,
1147147,
1151158,
1155176,
1159201,
1163233,
1167272,
1171318,
1175371,
1179431,
1183498,
1187572,
1191653,
1195741,
1199836,
1203938,
1208047,
1212163,
1216286,
1220416,
1224553,
1228697,
1232848,
1237006,
1241171,
1245343,
1249522,
1253708,
1257901.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 16903085 values, from 1 to 999999929649491).
n\r | 0 | 1 |
2 | 8451542 | 8451543 | 2 |
3 | 0 | 11268723 | 5634362 | 3 |
4 | 4225771 | 4225771 | 4225771 | 4225772 | 4 |
5 | 0 | 6761234 | 3380617 | 6761234 | 0 | 5 |
6 | 0 | 5634362 | 2817181 | 0 | 5634361 | 2817181 | 6 |
7 | 0 | 16903085 | 0 | 0 | 0 | 0 | 0 | 7 |
8 | 2112885 | 2112885 | 2112886 | 2112886 | 2112886 | 2112886 | 2112885 | 2112886 | 8 |
9 | 0 | 3756241 | 0 | 0 | 3756241 | 0 | 0 | 3756241 | 5634362 | 9 |
10 | 0 | 3380618 | 1690309 | 3380617 | 0 | 0 | 3380616 | 1690308 | 3380617 | 0 | 10 |
11 | 3073288 | 3073289 | 0 | 0 | 0 | 3073288 | 0 | 1536644 | 3073288 | 0 | 3073288 |
A pictorial representation of the table above
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.