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

1,7

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.

Links

Table of n, a(n) for n=1..109.

Prog

(PARI) k=1; while(k^2<n, if(isprime(n-k^2)&&isprime(n+k^2), return(k)); k++); 0
vector(50, n, a(n)) \\ Derek Orr, Feb 11 2015

Crossrefs

Cf. A068501, A082467, A178659.

Sequence in context: A343632 A067109 A237584 * A030219 A287345 A260675

Adjacent sequences: A254883 A254884 A254885 * A254887 A254888 A254889

Keyword

nonn

Author

Zak Seidov, Feb 10 2015

Status

approved