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

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.
a(9) = 0 since 9^2 + 2^2 = 85 is not prime.

Mathematica

f[n_] := If[OddQ[n] && ! PrimeQ[n^2 + 4], 0,
  Block[{p = 2}, While[! PrimeQ[n^2 + p^2] && p < 1500, p = NextPrime@p];
   p]]; Array[f, 100]

Crossrefs

Cf. A240130, A240131, A263466, A263721, A263722, A263726, A263977.

Sequence in context: A258581 A108501 A166226 * A326810 A263726 A328317

Adjacent sequences: A263975 A263976 A263977 * A263979 A263980 A263981

Keyword

nonn

Author

Jonathan Sondow and Robert G. Wilson v, Nov 06 2015

Status

approved