A263978 - OEIS

A263978

Least prime p such that n^2 + p^2 is prime, or 0 if none.

2, 3, 2, 5, 2, 5, 2, 3, 0, 3, 0, 7, 2, 11, 2, 5, 2, 5, 0, 3, 0, 5, 0, 5, 0, 5, 2, 5, 0, 11, 0, 3, 2, 5, 2, 5, 2, 3, 0, 3, 0, 5, 0, 19, 2, 5, 2, 13, 0, 7, 0, 3, 0, 11, 0, 11, 2, 3, 0, 13, 0, 3, 0, 11, 2, 29, 2, 5, 0, 3, 0, 5, 2, 5, 0, 5, 0, 7, 0, 7, 0, 3, 0, 11, 2, 11, 2, 3, 0, 11, 0, 7, 0, 5, 2, 5, 2, 3, 0, 3

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OFFSET

1,1

COMMENTS

When n is odd, n^2 + p^2 is composite for all odd primes p, so a(n) = 2 or 0 according as n^2 + 2^2 is prime or not.

The locations of the zeros are in A263722.

The location of the first occurrence of prime(n) is A263466(n).

LINKS

Table of n, a(n) for n=1..100.

EXAMPLE

a(1) = 2 since 1^2 + 2^2 = 5 is prime.

a(2) = 3 since 2^2 + 2^2 = 8 is not prime but 2^2 + 3^2 = 13 is prime.