A figurate number of form n(5n-3)/2. more
The first 600 heptagonal numbers :
1,
7,
18,
34,
55,
81,
112,
148,
189,
235,
286,
342,
403,
469,
540,
616,
697,
783,
874,
970,
1071,
1177,
1288,
1404,
1525,
1651,
1782,
1918,
2059,
2205,
2356,
2512,
2673,
2839,
3010,
3186,
3367,
3553,
3744,
3940,
4141,
4347,
4558,
4774,
4995,
5221,
5452,
5688,
5929,
6175,
6426,
6682,
6943,
7209,
7480,
7756,
8037,
8323,
8614,
8910,
9211,
9517,
9828,
10144,
10465,
10791,
11122,
11458,
11799,
12145,
12496,
12852,
13213,
13579,
13950,
14326,
14707,
15093,
15484,
15880,
16281,
16687,
17098,
17514,
17935,
18361,
18792,
19228,
19669,
20115,
20566,
21022,
21483,
21949,
22420,
22896,
23377,
23863,
24354,
24850,
25351,
25857,
26368,
26884,
27405,
27931,
28462,
28998,
29539,
30085,
30636,
31192,
31753,
32319,
32890,
33466,
34047,
34633,
35224,
35820,
36421,
37027,
37638,
38254,
38875,
39501,
40132,
40768,
41409,
42055,
42706,
43362,
44023,
44689,
45360,
46036,
46717,
47403,
48094,
48790,
49491,
50197,
50908,
51624,
52345,
53071,
53802,
54538,
55279,
56025,
56776,
57532,
58293,
59059,
59830,
60606,
61387,
62173,
62964,
63760,
64561,
65367,
66178,
66994,
67815,
68641,
69472,
70308,
71149,
71995,
72846,
73702,
74563,
75429,
76300,
77176,
78057,
78943,
79834,
80730,
81631,
82537,
83448,
84364,
85285,
86211,
87142,
88078,
89019,
89965,
90916,
91872,
92833,
93799,
94770,
95746,
96727,
97713,
98704,
99700,
100701,
101707,
102718,
103734,
104755,
105781,
106812,
107848,
108889,
109935,
110986,
112042,
113103,
114169,
115240,
116316,
117397,
118483,
119574,
120670,
121771,
122877,
123988,
125104,
126225,
127351,
128482,
129618,
130759,
131905,
133056,
134212,
135373,
136539,
137710,
138886,
140067,
141253,
142444,
143640,
144841,
146047,
147258,
148474,
149695,
150921,
152152,
153388,
154629,
155875,
157126,
158382,
159643,
160909,
162180,
163456,
164737,
166023,
167314,
168610,
169911,
171217,
172528,
173844,
175165,
176491,
177822,
179158,
180499,
181845,
183196,
184552,
185913,
187279,
188650,
190026,
191407,
192793,
194184,
195580,
196981,
198387,
199798,
201214,
202635,
204061,
205492,
206928,
208369,
209815,
211266,
212722,
214183,
215649,
217120,
218596,
220077,
221563,
223054,
224550,
226051,
227557,
229068,
230584,
232105,
233631,
235162,
236698,
238239,
239785,
241336,
242892,
244453,
246019,
247590,
249166,
250747,
252333,
253924,
255520,
257121,
258727,
260338,
261954,
263575,
265201,
266832,
268468,
270109,
271755,
273406,
275062,
276723,
278389,
280060,
281736,
283417,
285103,
286794,
288490,
290191,
291897,
293608,
295324,
297045,
298771,
300502,
302238,
303979,
305725,
307476,
309232,
310993,
312759,
314530,
316306,
318087,
319873,
321664,
323460,
325261,
327067,
328878,
330694,
332515,
334341,
336172,
338008,
339849,
341695,
343546,
345402,
347263,
349129,
351000,
352876,
354757,
356643,
358534,
360430,
362331,
364237,
366148,
368064,
369985,
371911,
373842,
375778,
377719,
379665,
381616,
383572,
385533,
387499,
389470,
391446,
393427,
395413,
397404,
399400,
401401,
403407,
405418,
407434,
409455,
411481,
413512,
415548,
417589,
419635,
421686,
423742,
425803,
427869,
429940,
432016,
434097,
436183,
438274,
440370,
442471,
444577,
446688,
448804,
450925,
453051,
455182,
457318,
459459,
461605,
463756,
465912,
468073,
470239,
472410,
474586,
476767,
478953,
481144,
483340,
485541,
487747,
489958,
492174,
494395,
496621,
498852,
501088,
503329,
505575,
507826,
510082,
512343,
514609,
516880,
519156,
521437,
523723,
526014,
528310,
530611,
532917,
535228,
537544,
539865,
542191,
544522,
546858,
549199,
551545,
553896,
556252,
558613,
560979,
563350,
565726,
568107,
570493,
572884,
575280,
577681,
580087,
582498,
584914,
587335,
589761,
592192,
594628,
597069,
599515,
601966,
604422,
606883,
609349,
611820,
614296,
616777,
619263,
621754,
624250,
626751,
629257,
631768,
634284,
636805,
639331,
641862,
644398,
646939,
649485,
652036,
654592,
657153,
659719,
662290,
664866,
667447,
670033,
672624,
675220,
677821,
680427,
683038,
685654,
688275,
690901,
693532,
696168,
698809,
701455,
704106,
706762,
709423,
712089,
714760,
717436,
720117,
722803,
725494,
728190,
730891,
733597,
736308,
739024,
741745,
744471,
747202,
749938,
752679,
755425,
758176,
760932,
763693,
766459,
769230,
772006,
774787,
777573,
780364,
783160,
785961,
788767,
791578,
794394,
797215,
800041,
802872,
805708,
808549,
811395,
814246,
817102,
819963,
822829,
825700,
828576,
831457,
834343,
837234,
840130,
843031,
845937,
848848,
851764,
854685,
857611,
860542,
863478,
866419,
869365,
872316,
875272,
878233,
881199,
884170,
887146,
890127,
893113,
896104,
899100.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 20000000 values, from 1 to 999999970000000).
n\r | 0 | 1 |
2 | 10000000 | 10000000 | 2 |
3 | 6666666 | 13333334 | 0 | 3 |
4 | 5000000 | 5000000 | 5000000 | 5000000 | 4 |
5 | 4000000 | 4000000 | 4000000 | 4000000 | 4000000 | 5 |
6 | 3333333 | 6666667 | 0 | 3333333 | 6666667 | 0 | 6 |
7 | 5714285 | 2857143 | 0 | 0 | 5714286 | 0 | 5714286 | 7 |
8 | 2500000 | 2500000 | 2500000 | 2500000 | 2500000 | 2500000 | 2500000 | 2500000 | 8 |
9 | 6666666 | 4444445 | 0 | 0 | 4444444 | 0 | 0 | 4444445 | 0 | 9 |
10 | 2000000 | 2000000 | 2000000 | 2000000 | 2000000 | 2000000 | 2000000 | 2000000 | 2000000 | 2000000 | 10 |
11 | 3636363 | 3636364 | 3636364 | 0 | 3636363 | 1818182 | 0 | 3636364 | 0 | 0 | 0 |
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.