A361999 -id:A361999 - cp's OEIS frontend

A361902 Least k such that n+A000045(k) is prime, or -1 if no such k exists.

3, 1, 0, 0, 1, 0, 1, 0, 4, 3, 1, 0, 1, 0, 4, 3, 1, 0, 1, 0, 4, 3, 1, 0, 5, 9, 4, 3, 1, 0, 1, 0, 5, 6, 4, 3, 1, 0, 4, 3, 1, 0, 1, 0, 4, 3, 1, 0, 5, 9, 4, 3, 1, 0, 5, 9, 4, 3, 1, 0, 1, 0, 5, 6, 4, 3, 1, 0, 4, 3, 1, 0, 1, 0, 5, 6, 4, 3, 1, 0, 4, 3, 1, 0, 5, 12, 4

Offset: 0

Pontus von Brömssen, Mar 28 2023

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Suggested by A361509.
2 does not appear because A000045(1) = A000045(2).
When n >= 3 and a(n) != -1, a(n) is divisible by 3 if and only if n is odd, because A000045(k) is even if and only if k is divisible by 3.
The least n for which a(n) = -1 is one of 7123, 11009, and 14475. When n is 7123 or 11009, either a(n) > 60000 or a(n) = -1.

			The first Fibonacci number F such that 25+F is prime is F = 34 = A000045(9), so a(25) = 9.

Pontus von Brömssen, Table of n, a(n) for n = 0..7122
Robert Gerbicz, Re: Add a Fibonacci number to get a prime, SeqFan mailing list, March 28, 2023.

Cf. A000045, A067760, A322004 (negative n), A361509, A361510, A361997 (records), A361998 (indices of records), A361999 (first occurrences).

a[n_] := Module[{k = 0}, While[! PrimeQ[n + Fibonacci[k]], k++]; k]; Array[a, 100, 0] (* Amiram Eldar, Mar 30 2023 *)

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

from sympy import isprime,fibonacci
from itertools import count
def A361902(n):
    # Note: the function hangs if a(n) = -1.
    return next(k for k in count() if isprime(n+fibonacci(k)))

a(n) = 0 if and only if n is prime.

a(n) = -1 if n == 14475 (mod m), where m = 2*3*5*7*11*23*31 = 1647030 (see Gerbicz link).

A363536 a(n) is the smallest k such that A363533(k) = n, or -1 if no such k exists.

Original entry on oeis.org

1, -1, 3, 24, 38, 17, 142, 248, 7, 328, 528, 67, 446, 1676, 31, 208, 1828, 25, 656, 788, 203, 4700, 1678, 47, 5368, 1270, 87, 2992, 10712, 317, 12034, 9262, 121, 5248, 11744, 61, 2798, 19598, 481, 3628, 8956, 181, 4388, 18694, 383, 22754, 23836, 43, 8212, 34636

Offset: 1

Pontus von Brömssen, Jun 09 2023

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Cf. A361999, A363533.

cp's OEIS Frontend

A361902 Least k such that n+A000045(k) is prime, or -1 if no such k exists.

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A363536 a(n) is the smallest k such that A363533(k) = n, or -1 if no such k exists.

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