A composite number n which divides the repunit Rn-1. more
The first 600 deceptive numbers :
91,
259,
451,
481,
703,
1729,
2821,
2981,
3367,
4141,
4187,
5461,
6533,
6541,
6601,
7471,
7777,
8149,
8401,
8911,
10001,
11111,
12403,
13981,
14701,
14911,
15211,
15841,
19201,
21931,
22321,
24013,
24661,
27613,
29341,
34133,
34441,
35113,
38503,
41041,
45527,
46657,
48433,
50851,
50881,
52633,
54913,
57181,
63139,
63973,
65311,
66991,
67861,
68101,
75361,
79003,
82513,
83119,
94139,
95161,
97273,
97681,
100001,
101101,
101491,
102173,
108691,
113201,
115627,
115921,
118301,
118957,
122221,
126217,
128713,
130351,
131821,
134821,
134863,
137137,
137149,
138481,
139231,
145181,
147001,
148417,
152551,
158497,
162401,
164761,
166499,
170017,
172081,
179881,
188191,
188269,
188461,
188501,
196651,
201917,
216001,
216931,
225589,
226273,
229633,
231337,
234421,
237169,
237817,
245491,
247753,
248677,
250717,
251251,
252601,
253099,
269011,
269569,
274231,
281821,
286903,
287749,
287809,
294409,
298033,
301081,
302177,
304057,
314821,
334153,
340561,
341503,
346801,
351809,
357641,
364277,
366337,
372731,
385003,
390313,
391141,
399001,
401401,
410041,
413339,
420343,
437251,
451091,
455971,
458641,
463241,
463489,
481601,
488881,
489997,
491063,
492101,
497377,
497503,
497927,
505363,
507529,
509971,
511969,
512461,
520801,
522349,
530881,
532171,
552721,
567721,
585631,
586993,
588193,
589537,
595231,
597871,
601657,
603961,
607321,
632641,
634351,
642001,
658801,
665401,
670033,
679861,
710533,
721801,
736291,
741751,
748657,
749521,
754369,
764491,
765703,
827281,
838201,
841633,
847693,
852841,
853381,
868001,
873181,
880237,
886033,
903169,
906193,
909709,
924001,
929633,
963857,
974611,
976873,
981317,
989017,
997633,
997981,
999001,
1004329,
1005697,
1024651,
1033669,
1038331,
1039441,
1039849,
1041043,
1042417,
1056331,
1069993,
1080697,
1081649,
1082809,
1090051,
1096681,
1111111,
1128871,
1141141,
1146401,
1152271,
1163801,
1167607,
1168513,
1169101,
1171261,
1182721,
1193221,
1242241,
1242571,
1251949,
1267801,
1268551,
1272271,
1275347,
1279201,
1287937,
1294411,
1298737,
1306369,
1308853,
1336699,
1362061,
1376299,
1394171,
1398101,
1408849,
1419607,
1446241,
1446661,
1450483,
1461241,
1462441,
1463749,
1492663,
1498981,
1504321,
1531711,
1543381,
1551941,
1569457,
1576381,
1583821,
1590751,
1602601,
1615681,
1703221,
1705621,
1708993,
1711381,
1711601,
1719601,
1731241,
1739089,
1748921,
1756351,
1758121,
1769377,
1772611,
1773289,
1792081,
1803413,
1809697,
1810513,
1826209,
1840321,
1846681,
1850017,
1857241,
1863907,
1869211,
1876393,
1884961,
1887271,
1892143,
1894651,
1907851,
1909001,
1918201,
1922801,
1926761,
1942957,
1943341,
1945423,
1953671,
1991821,
2024641,
2030341,
2044657,
2056681,
2063971,
2085301,
2100901,
2113921,
2146957,
2161501,
2165801,
2171197,
2171401,
2184931,
2190931,
2194973,
2203321,
2205967,
2215291,
2237017,
2278001,
2290289,
2299081,
2305633,
2314201,
2337301,
2358533,
2371681,
2386141,
2392993,
2406401,
2424731,
2432161,
2433601,
2455921,
2463661,
2503501,
2508013,
2512441,
2524801,
2525909,
2539183,
2553061,
2563903,
2585701,
2603381,
2628073,
2630071,
2658433,
2694601,
2699431,
2704801,
2719981,
2765713,
2795519,
2824061,
2868097,
2879317,
2887837,
2899351,
2916511,
2949991,
2960497,
2976487,
2987167,
3005737,
3057601,
3076481,
3084577,
3117547,
3125281,
3140641,
3146221,
3167539,
3186821,
3209053,
3225601,
3247453,
3255907,
3270403,
3362083,
3367441,
3367771,
3369421,
3387781,
3398921,
3400013,
3426401,
3429889,
3471071,
3488041,
3506221,
3520609,
3523801,
3536821,
3537667,
3581761,
3593551,
3596633,
3658177,
3677741,
3678401,
3740737,
3781141,
3788851,
3815011,
3817681,
3828001,
3850771,
3862207,
3879089,
3898129,
3913003,
3930697,
3947777,
3985921,
4005001,
4010401,
4014241,
4040281,
4040881,
4064677,
4074907,
4077151,
4099439,
4100041,
4119301,
4151281,
4181921,
4182739,
4209661,
4225057,
4234021,
4255903,
4260301,
4316089,
4326301,
4335241,
4360801,
4363261,
4363661,
4372771,
4373461,
4415251,
4415581,
4454281,
4463641,
4469471,
4469551,
4499701,
4504501,
4543621,
4627441,
4630141,
4637617,
4762381,
4767841,
4784689,
4806061,
4863127,
4903921,
4909177,
4909411,
4909913,
4917781,
5031181,
5045401,
5049001,
5056051,
5122133,
5148001,
5160013,
5180593,
5197837,
5203471,
5216953,
5256091,
5271251,
5276993,
5292631,
5294521,
5308181,
5309161,
5310721,
5371651,
5379361,
5406787,
5427841,
5444489,
5474657,
5477641,
5478913,
5479201,
5481451,
5495023,
5502061,
5623409,
5690251,
5718721,
5780941,
5792851,
5804821,
5824711,
5834851,
5887189,
5892511,
5934391,
5943301,
5950501,
5956741,
5968873,
6049681,
6070201,
6096181,
6157601,
6167161,
6186403,
6189121,
6298513,
6313681,
6330721,
6339673,
6425851,
6457951,
6469789,
6539821,
6541657,
6544561,
6577081,
6724861,
6733693,
6738601,
6761041,
6774499,
6822541,
6830891,
6840001,
6868261,
6892249,
6906901,
6934951,
6969511,
6997981,
7027681,
7071181,
7200793,
7207057,
7207201,
7232321,
7262413,
7344947,
7406311,
7428421,
7434541,
7439641,
7455481,
7519441,
7521361,
7532713,
7596211,
7619521,
7624501,
7644673,
7648033,
7652101,
7678501,
7683397,
7686401,
7686647,
7756201,
7758601,
7765759,
7948081,
7968511,
7995169.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 35383 values, from 91 to 99985191041).
n\r | 0 | 1 |
2 | 0 | 35383 | 2 |
3 | 0 | 30821 | 4562 | 3 |
4 | 0 | 28731 | 0 | 6652 | 4 |
5 | 0 | 22923 | 4260 | 4589 | 3611 | 5 |
6 | 0 | 30821 | 0 | 0 | 0 | 4562 | 6 |
7 | 3633 | 13852 | 3267 | 3803 | 3298 | 3738 | 3792 | 7 |
8 | 0 | 20098 | 0 | 3391 | 0 | 8633 | 0 | 3261 | 8 |
9 | 0 | 17480 | 1540 | 0 | 6659 | 1525 | 0 | 6682 | 1497 | 9 |
10 | 0 | 22923 | 0 | 4589 | 0 | 0 | 0 | 4260 | 0 | 3611 | 10 |
11 | 4265 | 8296 | 2389 | 2399 | 2468 | 2531 | 2578 | 2522 | 2722 | 2311 | 2902 |
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.