A290283 Primes p such that A215458(p) is prime.

3, 5, 7, 11, 17, 19, 23, 101, 107, 109, 113, 163, 283, 311, 331, 347, 359, 701, 1153, 1597, 1621, 2063, 2437, 2909, 3319, 6011, 12829, 46147, 46471, 74219, 112297, 128411, 178693, 223759, 268841, 407821, 526763, 925391, 927763

Offset: 1

Author

Paul S. Vanderveen, Jul 25 2017

Keywords

• nonn
• more

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.

Examples

			A215458(3) = 7, A215458(5) = 11, A215458 (7) = 71 are all primes, hence 3, 5, 7 are in this sequence.
		

Crossrefs

Cf. A215458.

Programs

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 *)

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])