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A093307
k-th upper twin prime, where k is the n-th Fibonacci number.
0
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
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
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