A085909 Smallest prime p>prime(n) such that p+prime(n+1)-prime(n) is the next prime after p; or a(n)=0 if no such prime exists.

0, 5, 11, 13, 17, 19, 29, 37, 31, 41, 47, 43, 59, 67, 53, 61, 71, 73, 79, 101, 83, 97, 131, 359, 103, 107, 109, 137, 127, 293, 163, 151, 149, 181, 179, 157, 167, 193, 173, 233, 191, 241, 197, 223, 227, 211, 467, 229, 239, 277, 251, 269, 283, 257, 263, 271, 281

Offset

1,2

Comments

A001223(n) = A001223(A049084(a(n))); a(A001359(n)) = A001359(n+1); conjecture: a(n) > 0 for n > 1 (implies the twin prime conjecture). - Reinhard Zumkeller, Jan 26 2004

For n > 1, a(n) >= prime(n+1) and a(n) = prime(n+1) if prime(n+1) is a balanced prime (A006562). - Zak Seidov, Jun 03 2015

Links

Zak Seidov, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Prime Difference Function

Mathematica

a[1] = 0; a[n_] := For[p = Prime[n+1]; d = p - Prime[n], True, p = q, q = NextPrime[p]; If[d == q - p, Return[p]]]; (* Jean-François Alcover, Feb 24 2015 *)

Prog

(MATLAB) P = primes(5000); A = zeros(1, length(P)); D = P(2:end) - P(1:(length(P) - 1)); for i = 2:2:(max(D)); f = find(D == i); A(f(1:(length(f) - 1))) = P(f(2:end)); end; A(2:100) % David Wasserman, Jan 26 2004

Crossrefs

Cf. A085910, A001223, A049084, A001359, A006562.

Sequence in context: A230359 A161548 A090320 * A288450 A346416 A384396

Adjacent sequences: A085906 A085907 A085908 * A085910 A085911 A085912

Keyword

nonn

Author

Amarnath Murthy, Jul 09 2003

Extensions

More terms from Reinhard Zumkeller and David Wasserman, Jan 26 2004

Edited by N. J. A. Sloane, Oct 21 2008 at the suggestion of R. J. Mathar

Status

approved