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A085909
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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.
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4
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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Zak Seidov, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Prime Difference Function
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MATHEMATICA
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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 *)
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PROG
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(MATLAB program by D. Wasserman) 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)
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CROSSREFS
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Cf. A085910, A001223, A049084, A001359, A006562.
Sequence in context: A230359 A161548 A090320 * A288450 A346416 A272446
Adjacent sequences: A085906 A085907 A085908 * A085910 A085911 A085912
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy, Jul 09 2003
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EXTENSIONS
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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
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STATUS
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approved
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