A figurate number of form 3n(n-1) + 1. more
The first 600 hex numbers :
1,
7,
19,
37,
61,
91,
127,
169,
217,
271,
331,
397,
469,
547,
631,
721,
817,
919,
1027,
1141,
1261,
1387,
1519,
1657,
1801,
1951,
2107,
2269,
2437,
2611,
2791,
2977,
3169,
3367,
3571,
3781,
3997,
4219,
4447,
4681,
4921,
5167,
5419,
5677,
5941,
6211,
6487,
6769,
7057,
7351,
7651,
7957,
8269,
8587,
8911,
9241,
9577,
9919,
10267,
10621,
10981,
11347,
11719,
12097,
12481,
12871,
13267,
13669,
14077,
14491,
14911,
15337,
15769,
16207,
16651,
17101,
17557,
18019,
18487,
18961,
19441,
19927,
20419,
20917,
21421,
21931,
22447,
22969,
23497,
24031,
24571,
25117,
25669,
26227,
26791,
27361,
27937,
28519,
29107,
29701,
30301,
30907,
31519,
32137,
32761,
33391,
34027,
34669,
35317,
35971,
36631,
37297,
37969,
38647,
39331,
40021,
40717,
41419,
42127,
42841,
43561,
44287,
45019,
45757,
46501,
47251,
48007,
48769,
49537,
50311,
51091,
51877,
52669,
53467,
54271,
55081,
55897,
56719,
57547,
58381,
59221,
60067,
60919,
61777,
62641,
63511,
64387,
65269,
66157,
67051,
67951,
68857,
69769,
70687,
71611,
72541,
73477,
74419,
75367,
76321,
77281,
78247,
79219,
80197,
81181,
82171,
83167,
84169,
85177,
86191,
87211,
88237,
89269,
90307,
91351,
92401,
93457,
94519,
95587,
96661,
97741,
98827,
99919,
101017,
102121,
103231,
104347,
105469,
106597,
107731,
108871,
110017,
111169,
112327,
113491,
114661,
115837,
117019,
118207,
119401,
120601,
121807,
123019,
124237,
125461,
126691,
127927,
129169,
130417,
131671,
132931,
134197,
135469,
136747,
138031,
139321,
140617,
141919,
143227,
144541,
145861,
147187,
148519,
149857,
151201,
152551,
153907,
155269,
156637,
158011,
159391,
160777,
162169,
163567,
164971,
166381,
167797,
169219,
170647,
172081,
173521,
174967,
176419,
177877,
179341,
180811,
182287,
183769,
185257,
186751,
188251,
189757,
191269,
192787,
194311,
195841,
197377,
198919,
200467,
202021,
203581,
205147,
206719,
208297,
209881,
211471,
213067,
214669,
216277,
217891,
219511,
221137,
222769,
224407,
226051,
227701,
229357,
231019,
232687,
234361,
236041,
237727,
239419,
241117,
242821,
244531,
246247,
247969,
249697,
251431,
253171,
254917,
256669,
258427,
260191,
261961,
263737,
265519,
267307,
269101,
270901,
272707,
274519,
276337,
278161,
279991,
281827,
283669,
285517,
287371,
289231,
291097,
292969,
294847,
296731,
298621,
300517,
302419,
304327,
306241,
308161,
310087,
312019,
313957,
315901,
317851,
319807,
321769,
323737,
325711,
327691,
329677,
331669,
333667,
335671,
337681,
339697,
341719,
343747,
345781,
347821,
349867,
351919,
353977,
356041,
358111,
360187,
362269,
364357,
366451,
368551,
370657,
372769,
374887,
377011,
379141,
381277,
383419,
385567,
387721,
389881,
392047,
394219,
396397,
398581,
400771,
402967,
405169,
407377,
409591,
411811,
414037,
416269,
418507,
420751,
423001,
425257,
427519,
429787,
432061,
434341,
436627,
438919,
441217,
443521,
445831,
448147,
450469,
452797,
455131,
457471,
459817,
462169,
464527,
466891,
469261,
471637,
474019,
476407,
478801,
481201,
483607,
486019,
488437,
490861,
493291,
495727,
498169,
500617,
503071,
505531,
507997,
510469,
512947,
515431,
517921,
520417,
522919,
525427,
527941,
530461,
532987,
535519,
538057,
540601,
543151,
545707,
548269,
550837,
553411,
555991,
558577,
561169,
563767,
566371,
568981,
571597,
574219,
576847,
579481,
582121,
584767,
587419,
590077,
592741,
595411,
598087,
600769,
603457,
606151,
608851,
611557,
614269,
616987,
619711,
622441,
625177,
627919,
630667,
633421,
636181,
638947,
641719,
644497,
647281,
650071,
652867,
655669,
658477,
661291,
664111,
666937,
669769,
672607,
675451,
678301,
681157,
684019,
686887,
689761,
692641,
695527,
698419,
701317,
704221,
707131,
710047,
712969,
715897,
718831,
721771,
724717,
727669,
730627,
733591,
736561,
739537,
742519,
745507,
748501,
751501,
754507,
757519,
760537,
763561,
766591,
769627,
772669,
775717,
778771,
781831,
784897,
787969,
791047,
794131,
797221,
800317,
803419,
806527,
809641,
812761,
815887,
819019,
822157,
825301,
828451,
831607,
834769,
837937,
841111,
844291,
847477,
850669,
853867,
857071,
860281,
863497,
866719,
869947,
873181,
876421,
879667,
882919,
886177,
889441,
892711,
895987,
899269,
902557,
905851,
909151,
912457,
915769,
919087,
922411,
925741,
929077,
932419,
935767,
939121,
942481,
945847,
949219,
952597,
955981,
959371,
962767,
966169,
969577,
972991,
976411,
979837,
983269,
986707,
990151,
993601,
997057,
1000519,
1003987,
1007461,
1010941,
1014427,
1017919,
1021417,
1024921,
1028431,
1031947,
1035469,
1038997,
1042531,
1046071,
1049617,
1053169,
1056727,
1060291,
1063861,
1067437,
1071019,
1074607,
1078201.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 18257419 values, from 1 to 999999990852427).
n\r | 0 | 1 |
2 | 0 | 18257419 | 2 |
3 | 0 | 18257419 | 0 | 3 |
4 | 0 | 9128709 | 0 | 9128710 | 4 |
5 | 0 | 7302967 | 7302968 | 0 | 3651484 | 5 |
6 | 0 | 18257419 | 0 | 0 | 0 | 0 | 6 |
7 | 5216405 | 5216405 | 2608203 | 0 | 0 | 5216406 | 0 | 7 |
8 | 0 | 4564355 | 0 | 4564355 | 0 | 4564354 | 0 | 4564355 | 8 |
9 | 0 | 12171613 | 0 | 0 | 0 | 0 | 0 | 6085806 | 0 | 9 |
10 | 0 | 7302967 | 0 | 0 | 0 | 0 | 0 | 7302968 | 0 | 3651484 | 10 |
11 | 0 | 3319531 | 0 | 1659765 | 3319531 | 0 | 3319530 | 3319531 | 3319531 | 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.