OFFSET
1,1
COMMENTS
Primes p such that (2^p - (1/2 - (i * sqrt(7))/2)^p - (1/2 + (i * sqrt(7))/2)^p + 1)/2 is prime.
It is conjectured that there are infinitely many terms.
EXAMPLE
MAPLE
h := proc(n) option remember; `if`(n=0, 2, `if`(n=1, 1, h(n-1)-2*h(n-2))) end:
select(n->isprime((2^n-h(n)+1)/2), select(isprime, [$1..1000])); # Peter Luschny, Jul 26 2017
MATHEMATICA
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 *)
PROG
(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])
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Paul S. Vanderveen, Jul 25 2017
STATUS
approved