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A290283 Primes p such that A215458(p) is prime. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A139559 A158361 A048184 * A163420 A155489 A194099

Adjacent sequences:  A290280 A290281 A290282 * A290284 A290285 A290286

KEYWORD

nonn,more

AUTHOR

Paul S. Vanderveen, Jul 25 2017

STATUS

approved

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Last modified April 19 03:08 EDT 2019. Contains 322237 sequences. (Running on oeis4.)