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COMMENTS
Different from A216360: the first term missing in A216360 is a(27)=97.
Primes p such that x^59 = 2 has no solution mod p.
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7
709, 827, 1063, 1181, 1889, 2243, 2833, 3187, 3541, 3659, 4013, 4603, 4721, 4957, 5783, 6373, 6491, 7789, 7907, 8969, 9323, 9677, 10267, 10739, 11093, 11329, 11801, 12037, 12391, 13099, 13217, 13807, 14633, 14869, 16993, 19471, 20297, 20533
COMMENTS
This is not the same as "Primes congruent to 1 mod 59", A216315. The first missing number is A216315(27) = 11447. - Zak Seidov, Sep 03 2012
MATHEMATICA
Select[Prime[Range[PrimePi[21000]]], ! MemberQ[PowerMod[Range[#], 59, #], Mod[2, #]] &] (* Bruno Berselli, Sep 20 2012 *) ok[p_] := Reduce[Mod[x^59 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[2500]], ok] (* Vincenzo Librandi, Sep 20 2012 *)
PROG
(Magma) [p: p in PrimesUpTo(21000) | forall{x: x in ResidueClassRing(p) | x^59 ne 2}]; // Bruno Berselli, Sep 20 2012
Primes p congruent to 1 mod 59 such that x^59 = 2 has solution mod p.
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3
11447, 82129, 225499, 246739, 453239, 523213, 554129, 709417, 724639, 838037, 926183, 967129, 1001467, 1008547, 1015627, 1015981, 1028017, 1037929, 1108729, 1112623, 1115573, 1238411, 1310627, 1388743, 1509457, 1634183, 1638431, 1655659, 1687991, 1731887
COMMENTS
Corresponding smallest values of x: 123, 271, 1220, 3773, 320, 29908, 5838, 2102, 2536, 22761, 1068.
97, 696, 1911, 2091, 3841, 4434, 4696, 6012, 6141, 7102, 7849, 8196, 8487, 8547, 8607, 8610, 8712, 8796, 9396, 9429, 9454, 10495, 11107, 11769, 12792, 13849, 13885, 14031, 14305, 14677, 14691, 14874, 14979, 15411, 16195, 16579, 16741, 17292, 17701, 18441
Least prime p such that p = n (mod 59).
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0
709, 2, 3, 181, 5, 419, 7, 67, 127, 541, 11, 71, 13, 73, 251, 193, 17, 313, 19, 79, 139, 199, 23, 83, 379, 439, 263, 677, 29, 89, 31, 563, 151, 211, 271, 331, 37, 97, 157, 571, 41, 101, 43, 103, 163, 223, 47, 107, 167, 109, 523, 229, 53, 113, 173, 233, 293, 353
FORMULA
a(n) = n if n is a prime < 59.
MATHEMATICA
Table[Select[Prime[Range[1000]], Mod[#, 59] == n &, 1][[1]], {n, 58}] (* T. D. Noe, Sep 07 2012 *)
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