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deceptive numbers
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 
2035383 2 
30308214562 3 
402873106652 4 
5022923426045893611 5 
60308210004562 6 
736331385232673803329837383792 7 
8020098033910863303261 8 
90174801540066591525066821497 9 
1002292304589000426003611 10 
1142658296238923992468253125782522272223112902

A pictorial representation of the table above
motab
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.