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

1,1

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.

Links

Table of n, a(n) for n=1..39.

Example

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

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

Cf. A215458.

Sequence in context: A158361 A342692 A048184 * A163420 A155489 A194099

Adjacent sequences: A290280 A290281 A290282 * A290284 A290285 A290286

Keyword

nonn,more

Author

Paul S. Vanderveen, Jul 25 2017

Status

approved