A361509 a(n) = smallest Fibonacci number F(k) such that F(k) + F(n) is a prime, or -1 if no such F(k) exists.

2, 1, 1, 0, 0, 0, 3, 0, 2, 3, 34, 0, 5, 0, 2, 3, 34, 0, 987, 46368, 2584, 3, 2, 0, 13, 144

Offset

0,1

Comments

a(26) is currently unknown.

a(26) > 10^7000 if it is not -1. - Robert Israel, Apr 03 2023

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = A000045(A361902(A000045(n))) (unless A361902(A000045(n)) = -1). - Pontus von Brömssen, Mar 30 2023

Maple

with(combinat):
a:=[]; b:=[]; for n from 0 to 25 do
k:=0; t1:=fibonacci(n);
while not isprime( fibonacci(k)+t1) do k:=k+1; od:
a:=[op(a), fibonacci(k)]; b:=[op(b), k];
od:
a; # A361509
b; # A361510

Mathematica

a[n_] := Module[{fn = Fibonacci[n], k = 0}, While[! PrimeQ[fn + Fibonacci[k]], k++]; Fibonacci[k]]; Array[a, 26, 0] (* Amiram Eldar, Mar 30 2023 *)

Prog

(PARI) a(n) = my(k=0, fn=fibonacci(n)); while (!isprime(fn+fibonacci(k)), k++); fibonacci(k); \\ Michel Marcus, Mar 30 2023

Crossrefs

Cf. A000045, A361510, A361902.

Sequence in context: A209287 A025901 A204431 * A143809 A056559 A117200

Adjacent sequences: A361506 A361507 A361508 * A361510 A361511 A361512

Keyword

nonn,more,less

Author

Jack Braxton, Mar 26 2023

Extensions

Edited by N. J. A. Sloane, Mar 30 2023

Status

approved