A254886 a(n) = least k>0 such that n-k^2 and n+k^2 are both primes.

0, 0, 0, 1, 0, 1, 2, 0, 2, 0, 0, 1, 0, 3, 2, 0, 0, 1, 0, 3, 4, 3, 0, 0, 0, 0, 2, 3, 0, 1, 0, 3, 2, 0, 0, 5, 0, 3, 0, 0, 0, 1, 6, 0, 4, 0, 6, 5, 0, 3, 0, 3, 6, 5, 0, 0, 2, 0, 0, 1, 0, 3, 2, 0, 6, 0, 6, 0, 0, 3, 0, 1, 6, 0, 2, 0, 6, 5, 0, 3, 0, 0, 0, 5, 0, 9, 4, 3, 0, 7, 0, 3, 2, 0, 6, 0, 0, 3, 0, 9, 0, 1, 6, 0, 2, 0, 0, 1, 0

Offset: 1

Author

Zak Seidov, Feb 10 2015

Keywords

• nonn

Comments

If n is a square then a(n)=sqrt(n)-1 or 0.

Also if n is a square and a(n)=sqrt(n)-1 then sqrt(n) is a term in A178659.

First appearances of k for k=1..58 are at n = 4, 7, 14, 21, 36, 43, 90, 117, 86, 111, 210, 149, 768, 201, 236, 285, 468, 329, 366, 411, 446, 1137, 534, 647, 654, 807, 770, 885, 900, 911, 3090, 1665, 1192, 2415, 1296, 1313, 4212, 2163, 1600, 1671, 5448, 1769, 2040, 1941, 2054, 3207, 2214, 2333, 5340, 2601, 2792, 7725, 2814, 3095, 3054, 5913, 3442, 4377.

Among the first 10000 terms, the first missing values are 59, 79, 82, 83, 89, 91, 92, 94, 97, 98, 100.

Crossrefs

Cf. A068501, A082467, A178659.

Programs

PARI

k=1;while(k^2Derek Orr, Feb 11 2015