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A099000
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Indices k such that the k-th prime is a Fibonacci number.
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3
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1, 2, 3, 6, 24, 51, 251, 3121, 42613, 23023556, 143130479, 2602986161967491
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OFFSET
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1,2
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COMMENTS
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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)
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LINKS
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FORMULA
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MATHEMATICA
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PrimePi[Select[Fibonacci[Range[80]], PrimeQ]]
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PROG
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(PARI) print1("1, 2"); forprime(p=5, 47, if(isprime(fibonacci(p)), print1(", "primepi(fibonacci(p))))) \\ Charles R Greathouse IV, Aug 21 2011
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CROSSREFS
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Cf. A001605 (n-th Fibonacci number is prime), A005478 (Prime Fibonacci numbers).
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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