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

%I

%S 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,

%T 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,

%U 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

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

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

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

%C 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.

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

%o (PARI) k=1;while(k^2<n,if(isprime(n-k^2)&&isprime(n+k^2),return(k));k++);0

%o vector(50,n,a(n)) \\ _Derek Orr_, Feb 11 2015

%Y Cf. A068501, A082467, A178659.

%K nonn

%O 1,7

%A _Zak Seidov_, Feb 10 2015

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Last modified January 30 07:42 EST 2023. Contains 359942 sequences. (Running on oeis4.)