Figurate numbers of the form 5n(n-1) + 1. more
The first 600 centered decagonal numbers :
1,
11,
31,
61,
101,
151,
211,
281,
361,
451,
551,
661,
781,
911,
1051,
1201,
1361,
1531,
1711,
1901,
2101,
2311,
2531,
2761,
3001,
3251,
3511,
3781,
4061,
4351,
4651,
4961,
5281,
5611,
5951,
6301,
6661,
7031,
7411,
7801,
8201,
8611,
9031,
9461,
9901,
10351,
10811,
11281,
11761,
12251,
12751,
13261,
13781,
14311,
14851,
15401,
15961,
16531,
17111,
17701,
18301,
18911,
19531,
20161,
20801,
21451,
22111,
22781,
23461,
24151,
24851,
25561,
26281,
27011,
27751,
28501,
29261,
30031,
30811,
31601,
32401,
33211,
34031,
34861,
35701,
36551,
37411,
38281,
39161,
40051,
40951,
41861,
42781,
43711,
44651,
45601,
46561,
47531,
48511,
49501,
50501,
51511,
52531,
53561,
54601,
55651,
56711,
57781,
58861,
59951,
61051,
62161,
63281,
64411,
65551,
66701,
67861,
69031,
70211,
71401,
72601,
73811,
75031,
76261,
77501,
78751,
80011,
81281,
82561,
83851,
85151,
86461,
87781,
89111,
90451,
91801,
93161,
94531,
95911,
97301,
98701,
100111,
101531,
102961,
104401,
105851,
107311,
108781,
110261,
111751,
113251,
114761,
116281,
117811,
119351,
120901,
122461,
124031,
125611,
127201,
128801,
130411,
132031,
133661,
135301,
136951,
138611,
140281,
141961,
143651,
145351,
147061,
148781,
150511,
152251,
154001,
155761,
157531,
159311,
161101,
162901,
164711,
166531,
168361,
170201,
172051,
173911,
175781,
177661,
179551,
181451,
183361,
185281,
187211,
189151,
191101,
193061,
195031,
197011,
199001,
201001,
203011,
205031,
207061,
209101,
211151,
213211,
215281,
217361,
219451,
221551,
223661,
225781,
227911,
230051,
232201,
234361,
236531,
238711,
240901,
243101,
245311,
247531,
249761,
252001,
254251,
256511,
258781,
261061,
263351,
265651,
267961,
270281,
272611,
274951,
277301,
279661,
282031,
284411,
286801,
289201,
291611,
294031,
296461,
298901,
301351,
303811,
306281,
308761,
311251,
313751,
316261,
318781,
321311,
323851,
326401,
328961,
331531,
334111,
336701,
339301,
341911,
344531,
347161,
349801,
352451,
355111,
357781,
360461,
363151,
365851,
368561,
371281,
374011,
376751,
379501,
382261,
385031,
387811,
390601,
393401,
396211,
399031,
401861,
404701,
407551,
410411,
413281,
416161,
419051,
421951,
424861,
427781,
430711,
433651,
436601,
439561,
442531,
445511,
448501,
451501,
454511,
457531,
460561,
463601,
466651,
469711,
472781,
475861,
478951,
482051,
485161,
488281,
491411,
494551,
497701,
500861,
504031,
507211,
510401,
513601,
516811,
520031,
523261,
526501,
529751,
533011,
536281,
539561,
542851,
546151,
549461,
552781,
556111,
559451,
562801,
566161,
569531,
572911,
576301,
579701,
583111,
586531,
589961,
593401,
596851,
600311,
603781,
607261,
610751,
614251,
617761,
621281,
624811,
628351,
631901,
635461,
639031,
642611,
646201,
649801,
653411,
657031,
660661,
664301,
667951,
671611,
675281,
678961,
682651,
686351,
690061,
693781,
697511,
701251,
705001,
708761,
712531,
716311,
720101,
723901,
727711,
731531,
735361,
739201,
743051,
746911,
750781,
754661,
758551,
762451,
766361,
770281,
774211,
778151,
782101,
786061,
790031,
794011,
798001,
802001,
806011,
810031,
814061,
818101,
822151,
826211,
830281,
834361,
838451,
842551,
846661,
850781,
854911,
859051,
863201,
867361,
871531,
875711,
879901,
884101,
888311,
892531,
896761,
901001,
905251,
909511,
913781,
918061,
922351,
926651,
930961,
935281,
939611,
943951,
948301,
952661,
957031,
961411,
965801,
970201,
974611,
979031,
983461,
987901,
992351,
996811,
1001281,
1005761,
1010251,
1014751,
1019261,
1023781,
1028311,
1032851,
1037401,
1041961,
1046531,
1051111,
1055701,
1060301,
1064911,
1069531,
1074161,
1078801,
1083451,
1088111,
1092781,
1097461,
1102151,
1106851,
1111561,
1116281,
1121011,
1125751,
1130501,
1135261,
1140031,
1144811,
1149601,
1154401,
1159211,
1164031,
1168861,
1173701,
1178551,
1183411,
1188281,
1193161,
1198051,
1202951,
1207861,
1212781,
1217711,
1222651,
1227601,
1232561,
1237531,
1242511,
1247501,
1252501,
1257511,
1262531,
1267561,
1272601,
1277651,
1282711,
1287781,
1292861,
1297951,
1303051,
1308161,
1313281,
1318411,
1323551,
1328701,
1333861,
1339031,
1344211,
1349401,
1354601,
1359811,
1365031,
1370261,
1375501,
1380751,
1386011,
1391281,
1396561,
1401851,
1407151,
1412461,
1417781,
1423111,
1428451,
1433801,
1439161,
1444531,
1449911,
1455301,
1460701,
1466111,
1471531,
1476961,
1482401,
1487851,
1493311,
1498781,
1504261,
1509751,
1515251,
1520761,
1526281,
1531811,
1537351,
1542901,
1548461,
1554031,
1559611,
1565201,
1570801,
1576411,
1582031,
1587661,
1593301,
1598951,
1604611,
1610281,
1615961,
1621651,
1627351,
1633061,
1638781,
1644511,
1650251,
1656001,
1661761,
1667531,
1673311,
1679101,
1684901,
1690711,
1696531,
1702361,
1708201,
1714051,
1719911,
1725781,
1731661,
1737551,
1743451,
1749361,
1755281,
1761211,
1767151,
1773101,
1779061,
1785031,
1791011,
1797001.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 14142136 values, from 1 to 999999982501801).
n\r | 0 | 1 |
2 | 0 | 14142136 | 2 |
3 | 0 | 9428091 | 4714045 | 3 |
4 | 0 | 7071068 | 0 | 7071068 | 4 |
5 | 0 | 14142136 | 0 | 0 | 0 | 5 |
6 | 0 | 9428091 | 0 | 0 | 0 | 4714045 | 6 |
7 | 0 | 4040611 | 0 | 4040610 | 4040610 | 2020305 | 0 | 7 |
8 | 0 | 3535534 | 0 | 3535534 | 0 | 3535534 | 0 | 3535534 | 8 |
9 | 0 | 3142697 | 4714045 | 0 | 3142697 | 0 | 0 | 3142697 | 0 | 9 |
10 | 0 | 14142136 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 10 |
11 | 2571297 | 2571297 | 2571298 | 0 | 0 | 0 | 2571298 | 0 | 1285649 | 2571297 | 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.