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%I #21 Feb 20 2017 14:47:19
%S 21,201,267,321,369,459,537,651,669,699,723,753,1071,1113,1197,1203,
%T 1209,1323,1401,1503,1587,1647,1773,1791,1797,1917,1941,2007,2139,
%U 2223,2427,2493,2613,2733,2769,2787,2847,3147,3249,3267,3297,3399,3423,3441,3771
%N Numbers n such that n^10 - 10 is prime.
%C All of the numbers in this sequence are odd multiples of 3 and, thus, congruent to 3 (mod 6).
%C The tenth powers modulo 6 are 1, 4, 3, 4, 1, 0, ... (A070431). Subtracting 10 (still modulo 6), we get 3, 0, 5, 0, 3, 2, ... which means that only n = 3 mod 6 can produce a potential prime p = 5 mod 6.
%e 21^10 - 10 = 16679880978191 is prime. Thus, 21 is a member of this sequence.
%t Select[Range[1000], PrimeQ[#^10 - 10] &] (* _Alonso del Arte_, Mar 18 2014 *)
%o (Python)
%o import sympy
%o from sympy import isprime
%o {print(n) for n in range(10**4) if isprime(n**10-10)}
%o (PARI) is(n)=isprime(n^10-10) \\ _Charles R Greathouse IV_, Feb 20 2017
%Y Cf. A028870, A153974, A239413, A239414, A239415, A239416, A239417, A239347.
%K nonn
%O 1,1
%A _Derek Orr_, Mar 17 2014