A number that can be written as ab + ba for a, b > 1. more
The Leyland numbers up to 10
15 :
8,
17,
32,
54,
57,
100,
145,
177,
320,
368,
512,
593,
945,
1124,
1649,
2169,
2530,
4240,
5392,
6250,
7073,
8361,
16580,
18785,
20412,
23401,
32993,
60049,
65792,
69632,
93312,
94932,
131361,
178478,
262468,
268705,
397585,
423393,
524649,
533169,
1048976,
1058576,
1596520,
1647086,
1941760,
2012174,
2097593,
4194788,
4208945,
4785713,
7861953,
8389137,
9865625,
10609137,
14352282,
16777792,
16797952,
33554432,
33555057,
43050817,
45136576,
48989176,
61466176,
67109540,
67137425,
129145076,
134218457,
177264449,
244389457,
268436240,
268473872,
292475249,
364568617,
387426321,
536871753,
774840978,
1073742724,
1073792449,
1162268326,
1173741824,
1221074418,
1996813914,
2147484609,
2179768320,
3486792401,
4294968320,
4295032832,
4486784401,
6104053449,
8589935681,
8804293473,
10460362464,
13065520825,
13877119009,
17179870340,
17179952705,
20000000000,
30518337500,
31381070257,
33739007300,
34359739593,
68719478032,
68719581712,
69149458432,
78371693632,
94143190994,
96951758924,
125937424601,
137438954841,
152588939201,
274877908388,
274878037265,
282429550305,
287589316833,
470196375201,
549755815409,
550571544609,
570623341222,
678328486353,
762940872982,
847288625068,
1061917364224,
1099511629376,
1099511787776,
2199023257233,
2541865845905,
2552470327702,
2821126684672,
3814699155193,
3881436747409,
4398046512868,
4398046705585,
4399522300160,
4747732369318,
7625597504670,
8796093024057,
10137858491849,
16926683582305,
17592186046352,
17592186278672,
17832200896512,
19073488804224,
22876792476913,
22897453501745,
33233199005057,
35184372090857,
35186934979457,
36314872537968,
68630377389272,
70368744179780,
70368744457505,
95367434840625,
100289254654976,
101559990680640,
130291290501553,
140737488357537,
205891132121649,
205929575454024,
232630924325880,
281474976712960,
281474977042432,
281479271677952,
383799398752905,
476837162287226,
562949953423713,
605750213184506,
609359787056377,
617673396313738.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 116412 values, from 8 to 101000).
n\r | 0 | 1 |
2 | 58303 | 58109 | 2 |
3 | 32375 | 41398 | 42639 | 3 |
4 | 43947 | 58109 | 14356 | 0 | 4 |
5 | 25848 | 23881 | 28123 | 18770 | 19790 | 5 |
6 | 12662 | 18901 | 23144 | 19713 | 22497 | 19495 | 6 |
7 | 15164 | 18205 | 22455 | 17846 | 12636 | 16915 | 13191 | 7 |
8 | 35990 | 58109 | 7175 | 0 | 7957 | 0 | 7181 | 0 | 8 |
9 | 19377 | 39280 | 9766 | 6498 | 1061 | 9766 | 6500 | 1057 | 23107 | 9 |
10 | 14127 | 11385 | 16482 | 11674 | 8102 | 11721 | 12496 | 11641 | 7096 | 11688 | 10 |
11 | 9519 | 10202 | 13882 | 9699 | 12051 | 11245 | 11009 | 8647 | 9484 | 9088 | 11586 |
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.