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%I #19 Jul 28 2017 09:54:28
%S 3,5,7,11,17,19,23,101,107,109,113,163,283,311,331,347,359,701,1153,
%T 1597,1621,2063,2437,2909,3319,6011,12829,46147,46471,74219,112297,
%U 128411,178693,223759,268841,407821,526763,925391,927763
%N Primes p such that A215458(p) is prime.
%C Primes p such that (2^p - (1/2 - (i * sqrt(7))/2)^p - (1/2 + (i * sqrt(7))/2)^p + 1)/2 is prime.
%C It is conjectured that there are infinitely many terms.
%e A215458(3) = 7, A215458(5) = 11, A215458 (7) = 71 are all primes, hence 3, 5, 7 are in this sequence.
%p h := proc(n) option remember; `if`(n=0,2,`if`(n=1,1,h(n-1)-2*h(n-2))) end:
%p select(n->isprime((2^n-h(n)+1)/2),select(isprime,[$1..1000])); # _Peter Luschny_, Jul 26 2017
%t Function[s, Keys@ KeySelect[s, AllTrue[{#, Lookup[s, #]}, PrimeQ] &]]@ MapIndexed[First[#2] - 1 -> #1 &, LinearRecurrence[{4, -7, 8, -4}, {0, 1, 4, 7}, 7000]] (* _Michael De Vlieger_, Jul 26 2017 *)
%o (PARI) isprime(([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -4, 8, -7, 4]^n*[0; 1; 4; 7])[1, 1])
%Y Cf. A215458.
%K nonn,more
%O 1,1
%A _Paul S. Vanderveen_, Jul 25 2017
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