

A263978


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


1



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.
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 * A263726 A088167 A073893
Adjacent sequences: A263975 A263976 A263977 * A263979 A263980 A263981


KEYWORD

nonn


AUTHOR

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


STATUS

approved



