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A099000
Indices k such that the k-th prime is a Fibonacci number.
3
1, 2, 3, 6, 24, 51, 251, 3121, 42613, 23023556, 143130479, 2602986161967491
OFFSET
1,2
COMMENTS
From Hugo Pfoertner, Jan 06 2020: (Start)
The computation of the next two terms, corresponding to the primes F(131) = A005478(13) = 1066340417491710595814572169, and F(137) = A005478(14) = 19134702400093278081449423917, should already be within reach with current (2020) technology, e.g. with Kim Walisch's "primecount" program, which allows massive parallelization. An exact determination of the following term a(15), which corresponds to F(359), is beyond any imaginable technical possibility.
Estimates for a(13)-a(15), found by using the PARI program from A121046 in a bisection loop, with an accuracy that corresponds to the shown number of digits, are as follows:
a(13) = primepi(F(131)) ~= 1.741898800848...*10^25,
a(14) = primepi(F(137)) ~= 2.9848914766265...*10^26,
a(15) = primepi(F(359)) ~= 2.78114064956041656819790214151422895...*10^72.
(End)
FORMULA
a(n) = A000720(A005478(n)). - M. F. Hasler, Aug 21 2011
MATHEMATICA
PrimePi[Select[Fibonacci[Range[80]], PrimeQ]]
PROG
(PARI) print1("1, 2"); forprime(p=5, 47, if(isprime(fibonacci(p)), print1(", "primepi(fibonacci(p))))) \\ Charles R Greathouse IV, Aug 21 2011
CROSSREFS
Cf. A001605 (n-th Fibonacci number is prime), A005478 (Prime Fibonacci numbers).
Cf. A121046.
Sequence in context: A295967 A027163 A160683 * A032540 A063728 A333420
KEYWORD
nonn,hard,more
AUTHOR
Rick L. Shepherd, Nov 06 2004
EXTENSIONS
a(11) from Ryan Propper, Oct 16 2005
a(12) from Charles R Greathouse IV, Aug 21 2011
STATUS
approved