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%I #24 Sep 27 2024 13:20:33
%S 1,4,11,149
%N Indices of primes p such that 7^p - 2 is prime.
%C Except for p=2, 2, 5^p - 2 cannot be prime. This immediately follows from the fact that a number N = (3k+2)^p - 2 cannot be prime for p > 2 because N = 3H + 2^p - 2 = 3H + 2(2^(p-1)-1) is divisible by 3.
%C a(5) > 8742, if it exists (cf. _J.W.L. (Jan) Eerland_'s comment in A147782). - _Amiram Eldar_, Jul 07 2024
%C a(5) > 23967, if it exists (using A090669). - _Michael S. Branicky_, Aug 17 2024
%F a(n) = A000720(A147782(n)). - _Amiram Eldar_, Jul 07 2024
%t Select[Range[500],PrimeQ[7^Prime[#]-2]&] (* _Harvey P. Dale_, May 02 2011 *)
%t Position[Prime[Range[150]],_?(PrimeQ[7^#-2]&)]//Flatten (* _Harvey P. Dale_, May 11 2016 *)
%o (PARI) forprime(p=2,1e4,if(ispseudoprime(7^p-2),print1(x",")))
%Y Cf. A147782 (primes p such that 7^p - 2 is prime), A000720, A090669.
%K nonn,more
%O 1,2
%A _Cino Hilliard_, Jan 11 2004
%E Definition clarified by Harvey P. Dale, May 02 2011.