A093307 k-th upper twin prime, where k is the n-th Fibonacci number.

5, 5, 7, 13, 31, 73, 181, 349, 859, 1723, 3361, 6091, 11833, 22273, 41959, 77713, 138403, 249439, 447793, 799741, 1399201, 2459923, 4312741, 7581943, 13233841, 23019043, 39921979, 69112963, 119168383, 205190353, 352286899, 603678289, 1032646423, 1763797501

Offset

1,1

Links

Table of n, a(n) for n=1..34.

Formula

a(n) = 2 + A093306(n) = A006512(A000045(n)). - R. J. Mathar, Feb 06 2010

Mathematica

Module[{nn=10^7, fibs, twns}, twns=Select[Partition[Prime[Range[nn]], 2, 1], #[[2]]-#[[1]]==2&][[;; , 2]]; fibs=Fibonacci[Range[Floor[Log[GoldenRatio, Sqrt[5]Max[Length[twns]]]]]]; Table[Take[twns, {f, f}], {f, fibs}]]//Flatten  (* Harvey P. Dale, Apr 05 2023 *)

Prog

(PARI) g(n) = for(x=1, n, print1(twinu(fibonacci(x))", ")) twinu(n) = { local(c, x); c=0; x=1; while(c<n, if(isprime(prime(x)+2), c++); x++; ); return(prime(x)) }
(PARI) default(primelimit, 20000000); twinu(n) = { local(c, x); c=0; x=1; while(c<n, if(isprime(prime(x)+2), c++); x++); return(prime(x)) } { for(n=1, 25, write("b093307.txt", n, " ", twinu(fibonacci(n)))); } \\ Harry J. Smith, Jun 20 2009

Crossrefs

Cf. A000045, A006512, A093306.

Sequence in context: A247877 A252006 A158299 * A264388 A141392 A088047

Adjacent sequences: A093304 A093305 A093306 * A093308 A093309 A093310

Keyword

nonn

Author

Cino Hilliard, Apr 25 2004

Extensions

a(24)-a(25) from Harry J. Smith, Jun 20 2009

a(26)-a(34) from Giovanni Resta, Jun 10 2018

Status

approved