A figurate number of form n(7n-5)/2. more
The first 600 nonagonal numbers :
1,
9,
24,
46,
75,
111,
154,
204,
261,
325,
396,
474,
559,
651,
750,
856,
969,
1089,
1216,
1350,
1491,
1639,
1794,
1956,
2125,
2301,
2484,
2674,
2871,
3075,
3286,
3504,
3729,
3961,
4200,
4446,
4699,
4959,
5226,
5500,
5781,
6069,
6364,
6666,
6975,
7291,
7614,
7944,
8281,
8625,
8976,
9334,
9699,
10071,
10450,
10836,
11229,
11629,
12036,
12450,
12871,
13299,
13734,
14176,
14625,
15081,
15544,
16014,
16491,
16975,
17466,
17964,
18469,
18981,
19500,
20026,
20559,
21099,
21646,
22200,
22761,
23329,
23904,
24486,
25075,
25671,
26274,
26884,
27501,
28125,
28756,
29394,
30039,
30691,
31350,
32016,
32689,
33369,
34056,
34750,
35451,
36159,
36874,
37596,
38325,
39061,
39804,
40554,
41311,
42075,
42846,
43624,
44409,
45201,
46000,
46806,
47619,
48439,
49266,
50100,
50941,
51789,
52644,
53506,
54375,
55251,
56134,
57024,
57921,
58825,
59736,
60654,
61579,
62511,
63450,
64396,
65349,
66309,
67276,
68250,
69231,
70219,
71214,
72216,
73225,
74241,
75264,
76294,
77331,
78375,
79426,
80484,
81549,
82621,
83700,
84786,
85879,
86979,
88086,
89200,
90321,
91449,
92584,
93726,
94875,
96031,
97194,
98364,
99541,
100725,
101916,
103114,
104319,
105531,
106750,
107976,
109209,
110449,
111696,
112950,
114211,
115479,
116754,
118036,
119325,
120621,
121924,
123234,
124551,
125875,
127206,
128544,
129889,
131241,
132600,
133966,
135339,
136719,
138106,
139500,
140901,
142309,
143724,
145146,
146575,
148011,
149454,
150904,
152361,
153825,
155296,
156774,
158259,
159751,
161250,
162756,
164269,
165789,
167316,
168850,
170391,
171939,
173494,
175056,
176625,
178201,
179784,
181374,
182971,
184575,
186186,
187804,
189429,
191061,
192700,
194346,
195999,
197659,
199326,
201000,
202681,
204369,
206064,
207766,
209475,
211191,
212914,
214644,
216381,
218125,
219876,
221634,
223399,
225171,
226950,
228736,
230529,
232329,
234136,
235950,
237771,
239599,
241434,
243276,
245125,
246981,
248844,
250714,
252591,
254475,
256366,
258264,
260169,
262081,
264000,
265926,
267859,
269799,
271746,
273700,
275661,
277629,
279604,
281586,
283575,
285571,
287574,
289584,
291601,
293625,
295656,
297694,
299739,
301791,
303850,
305916,
307989,
310069,
312156,
314250,
316351,
318459,
320574,
322696,
324825,
326961,
329104,
331254,
333411,
335575,
337746,
339924,
342109,
344301,
346500,
348706,
350919,
353139,
355366,
357600,
359841,
362089,
364344,
366606,
368875,
371151,
373434,
375724,
378021,
380325,
382636,
384954,
387279,
389611,
391950,
394296,
396649,
399009,
401376,
403750,
406131,
408519,
410914,
413316,
415725,
418141,
420564,
422994,
425431,
427875,
430326,
432784,
435249,
437721,
440200,
442686,
445179,
447679,
450186,
452700,
455221,
457749,
460284,
462826,
465375,
467931,
470494,
473064,
475641,
478225,
480816,
483414,
486019,
488631,
491250,
493876,
496509,
499149,
501796,
504450,
507111,
509779,
512454,
515136,
517825,
520521,
523224,
525934,
528651,
531375,
534106,
536844,
539589,
542341,
545100,
547866,
550639,
553419,
556206,
559000,
561801,
564609,
567424,
570246,
573075,
575911,
578754,
581604,
584461,
587325,
590196,
593074,
595959,
598851,
601750,
604656,
607569,
610489,
613416,
616350,
619291,
622239,
625194,
628156,
631125,
634101,
637084,
640074,
643071,
646075,
649086,
652104,
655129,
658161,
661200,
664246,
667299,
670359,
673426,
676500,
679581,
682669,
685764,
688866,
691975,
695091,
698214,
701344,
704481,
707625,
710776,
713934,
717099,
720271,
723450,
726636,
729829,
733029,
736236,
739450,
742671,
745899,
749134,
752376,
755625,
758881,
762144,
765414,
768691,
771975,
775266,
778564,
781869,
785181,
788500,
791826,
795159,
798499,
801846,
805200,
808561,
811929,
815304,
818686,
822075,
825471,
828874,
832284,
835701,
839125,
842556,
845994,
849439,
852891,
856350,
859816,
863289,
866769,
870256,
873750,
877251,
880759,
884274,
887796,
891325,
894861,
898404,
901954,
905511,
909075,
912646,
916224,
919809,
923401,
927000,
930606,
934219,
937839,
941466,
945100,
948741,
952389,
956044,
959706,
963375,
967051,
970734,
974424,
978121,
981825,
985536,
989254,
992979,
996711,
1000450,
1004196,
1007949,
1011709,
1015476,
1019250,
1023031,
1026819,
1030614,
1034416,
1038225,
1042041,
1045864,
1049694,
1053531,
1057375,
1061226,
1065084,
1068949,
1072821,
1076700,
1080586,
1084479,
1088379,
1092286,
1096200,
1100121,
1104049,
1107984,
1111926,
1115875,
1119831,
1123794,
1127764,
1131741,
1135725,
1139716,
1143714,
1147719,
1151731,
1155750,
1159776,
1163809,
1167849,
1171896,
1175950,
1180011,
1184079,
1188154,
1192236,
1196325,
1200421,
1204524,
1208634,
1212751,
1216875,
1221006,
1225144,
1229289,
1233441,
1237600,
1241766,
1245939,
1250119,
1254306,
1258500.
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 999999946552575).
n\r | 0 | 1 |
2 | 8451542 | 8451543 | 2 |
3 | 11268723 | 5634362 | 0 | 3 |
4 | 4225771 | 4225772 | 4225771 | 4225771 | 4 |
5 | 3380617 | 6761234 | 0 | 0 | 6761234 | 5 |
6 | 5634361 | 2817181 | 0 | 5634362 | 2817181 | 0 | 6 |
7 | 2414726 | 2414727 | 2414727 | 2414727 | 2414726 | 2414726 | 2414726 | 7 |
8 | 2112885 | 2112886 | 2112886 | 2112885 | 2112886 | 2112886 | 2112885 | 2112886 | 8 |
9 | 3756241 | 5634362 | 0 | 3756241 | 0 | 0 | 3756241 | 0 | 0 | 9 |
10 | 1690308 | 3380617 | 0 | 0 | 3380617 | 1690309 | 3380617 | 0 | 0 | 3380617 | 10 |
11 | 3073288 | 3073289 | 3073288 | 0 | 0 | 0 | 3073288 | 0 | 1536644 | 3073288 | 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.