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, 4740217

Offset

1,1

Comments

Composed of terms k from A001605 such that A004090(k) is prime. - Max Alekseyev, Nov 06 2025

Links

Table of n, a(n) for n=1..9.

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

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

Subsequence of A001605.

Cf. A000045, 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

Extensions

a(9) from Max Alekseyev, Nov 05 2025

Status

approved