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, 1, 1, 3, 1, 2, 3, 2, 5, 1, 1, 3, 2, 4, 2, 3, 1, 6, 3, 4, 4, 2, 2, 3, 3, 5, 7, 3, 1, 1, 2, 2, 2, 1, 1, 3, 10, 3, 2, 1, 3, 3, 10, 7, 1, 3, 7, 7, 4, 9, 1, 1, 1, 8, 2, 1, 2, 1, 8, 4, 1, 3, 5, 5, 8, 6, 5, 2, 3, 2, 10, 4, 5, 3, 5, 1, 1, 2, 10, 1, 1, 4, 12, 4, 2, 2, 6, 5, 1, 2, 7, 1, 12, 4, 2

Offset

1,6

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

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

Example

a(n) = A260870((prime(n)-1)/2) for n > 1. - Robert Israel, Oct 10 2024, corrected by M. F. Hasler, Oct 10 2024

Maple

f:= proc(n) local p, k;
     p:= ithprime(n);
     for k from 1 to p do if isprime(k^2 + (p-k)^2) then return k fi od;
     0
end proc:
map(f, [$1..100]); # Robert Israel, Oct 10 2024

Prog

(PARI) A260869(n)=for(k=1, (n=prime(n))\2, isprime(k^2+(n-k)^2)&&return(k))
(Python)
from sympy import prime, isprime
def A260869(n):
    p = prime(n)
    return next((k for k in range(1, (p>>1)+1) if isprime(k**2+(p-k)**2)), 0) # Chai Wah Wu, Oct 14 2024

Crossrefs

Cf. A260870.

Sequence in context: A305391 A165084 A029279 * A274514 A342932 A026181

Adjacent sequences: A260866 A260867 A260868 * A260870 A260871 A260872

Keyword

nonn

Author

M. F. Hasler, Aug 09 2015

Extensions

Corrected by Robert Israel, Oct 10 2024

Status

approved