Voozh

A391207

The smallest nonnegative integer k such that n + k is not a sum of two squares.

2, 1, 0, 2, 1, 0, 0, 3, 2, 1, 0, 0, 1, 0, 0, 3, 2, 1, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 2, 1, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 2, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 3, 2, 1, 0, 0, 0, 0, 0, 3, 2, 1, 0, 0, 1, 0, 0

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OFFSET

1,1

COMMENTS

The value of a(n) is at most 3 since among 4 consecutive integers there is one congruent 3 modulo 4 and no such number is a sum of two squares.

LINKS

Table of n, a(n) for n=1..87.

PROG

(PARI) isSumOfTwoSquares(n) = { my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2] % 2 && f[i, 1] % 4 == 3, return(0))); 1 }

a(n) = { my(r=0); while(isSumOfTwoSquares(n+r), r=r+1); r }

CROSSREFS

Cf. A022544, A070176.