A260869 Least k > 0 such that k^2 + (prime(n)-k)^2 is a prime, or 0 if no such k exists.

1, 1, 1, 2, 1, 3, 1, 1, 2, 1, 3, 1, 1, 2, 5, 4, 2, 1, 2, 1, 3, 4, 2, 2, 5, 4, 1, 1, 2, 3, 5, 3, 1, 2, 6, 3, 1, 5, 4, 5, 4, 1, 2, 2, 1, 4, 1, 2, 2, 3, 3, 2, 5, 7, 1, 3, 3, 1, 2, 1, 4, 1, 1, 4, 1, 4, 1, 2, 2, 5, 3, 3, 1, 2, 1, 5, 4, 1, 5, 1, 3, 2, 10, 2, 1, 3, 6, 1, 2, 1, 4, 1, 5, 10, 3, 3, 2, 10, 7

Offset

1,4

Comments

It appears that any prime (and also any odd number > 1, see A260870) can be written as the sum of two positive integers such that the sum of their squares is prime. For an even number > 2 this is obviously not possible since k and 2n-k have the same parity and therefore the sum of their squares is even.

Links

Table of n, a(n) for n=1..99.

Prog

(PARI) A260869(n)=for(k=1, (n=prime(n))\2, isprime(k^2+(n-k)^2)&&return(k))

Crossrefs

Sequence in context: A058564 A226006 A210943 * A260870 A282497 A087157

Adjacent sequences: A260866 A260867 A260868 * A260870 A260871 A260872

Keyword

nonn

Author

M. F. Hasler, Aug 09 2015

Status

approved