A378898 a(n) is the least k > 0 such that (n+k)^2 + n^2 is prime.

1, 1, 5, 1, 1, 5, 1, 5, 1, 3, 3, 1, 7, 1, 7, 3, 1, 5, 1, 3, 5, 1, 7, 1, 1, 5, 5, 5, 1, 1, 13, 1, 7, 1, 1, 13, 3, 7, 1, 3, 3, 1, 5, 5, 7, 3, 1, 5, 25, 1, 5, 5, 5, 5, 3, 5, 11, 5, 5, 1, 3, 3, 17, 7, 1, 5, 13, 27, 1, 1, 13, 1, 27, 5, 19, 9, 3, 5, 1, 9, 19, 1, 5, 1, 1, 9, 1, 15, 7, 1, 3, 3, 5, 5, 7

Offset: 1

Author

Robert Israel, Dec 11 2024

Keywords

• nonn

Examples

			a(3) = 5 because (3+5)^2 + 3^2 = 73 is prime, and no smaller number works.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A027861 (a(n) = 1), A089489, A378945, A378946.

Programs

Maple

f:= proc(n) local k;
  for k from n+1 by 2 do
    if igcd(k,n) = 1 and isprime(k^2 + n^2) then return k-n fi
  od
end proc;
map(f, [$1..100]);

PARI

a(n) = my(k=1); while (!isprime((n+k)^2 + n^2), k++); k; \\ Michel Marcus, Dec 11 2024

Formula

a(n) = A089489(n) - n.