

A254886


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


0



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
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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(nk^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



