A319393 Indices of triple prime Fibonacci numbers: numbers k such that (1) Fibonacci(k) is prime, (2) k is prime, and (3) the sum of the digits of Fibonacci(k) is prime.

3, 5, 11, 29, 43, 47, 449, 104911

Offset

1,1

Comments

Fibonacci(104911), corresponding to the 8th term of the sequence, has 21925 digits.

a(9) > A001605(51) = 3340367. - Alois P. Heinz, Sep 18 2018

Links

Table of n, a(n) for n=1..8.

Formula

A000045(a(n)) = A319230(n).

Example

29 is a term of the sequence, since 29 is prime, Fibonacci(29) = A000045(29) = 514229 is prime and the digit sum of 514229 = A007953(514229) = 23 is also prime. - Felix Fröhlich, Sep 18 2018

Mathematica

Select[Prime[Range[100]], AllTrue[{Fibonacci[#], Total[ IntegerDigits[ Fibonacci[ #]]]}, PrimeQ] &] (* The program uses the AllTrue function from Mathematica version 10 *)

Prog

(PARI) is(n) = if(!ispseudoprime(n), return(0), my(f=fibonacci(n)); if(!ispseudoprime(sumdigits(f)), return(0), if(ispseudoprime(f), return(1), return(0)))) \\ Felix Fröhlich, Sep 18 2018

Crossrefs

Cf. A000045, A001605, A007953, A319230.

Sequence in context: A093706 A109945 A045536 * A019338 A292539 A046134

Adjacent sequences: A319390 A319391 A319392 * A319394 A319395 A319396

Keyword

nonn,base,hard,more

Author

Harvey P. Dale, Sep 18 2018

Status

approved