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%I #4 Oct 01 2013 17:57:37
%S 3,53,71,97,109,127,137,149,151,179,197,239,293,311,401,419,431,439,
%T 457,467,503,557,563,601,619,641,643,653,673,769,887,907,971,991,1021,
%U 1031,1093,1103,1123,1151,1297,1361,1367,1373,1427,1447,1459,1471,1481
%N First of four consecutive primes p, q, r, s such that neither of the congruences p^x+q^x = r (mod s) and q^x-p^x = r (mod s) has a solution.
%C Is this sequence infinite?
%F a(n) = prime(A082475(n)).
%e 2 is not in the sequence because 2^1+3^1 = 5 (mod 7).
%e 17 is not in the sequence because 19^4-17^4 = 23 (mod 29).
%o (PARI) { for (p = 1, 300, f = 0; for (x = 1, prime(p + 3) - 1, if ((prime(p + 1)^x + prime(p)^x - prime(p + 2))%prime(p + 3) == 0 || (prime(p + 1)^x - prime(p)^x - prime(p + 2))%prime(p + 3) == 0, f = 1; break)); if (f == 0, print(prime(p)))) }
%Y Cf. A082371, A082475.
%K easy,nonn,less
%O 1,1
%A _Cino Hilliard_, May 11 2003
%E Edited and extended by _David Wasserman_, Oct 12 2006
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