Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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