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

Author

Harvey P. Dale, Sep 18 2018

Keywords

• nonn
• base
• hard
• more

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

Examples

			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
		

Crossrefs

Cf. A000045, A001605, A007953, A319230.

Programs

Mathematica

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

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

Formula

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