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

Author

Amarnath Murthy, Jul 09 2003

Keywords

• nonn

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

Crossrefs

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

Programs

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

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 *)

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