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%I #26 Jul 17 2021 11:22:53
%S 3,5,11,29,43,47,449,104911
%N 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.
%C Fibonacci(104911), corresponding to the 8th term of the sequence, has 21925 digits.
%C a(9) > A001605(51) = 3340367. - _Alois P. Heinz_, Sep 18 2018
%F A000045(a(n)) = A319230(n).
%e 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
%t Select[Prime[Range[100]],AllTrue[{Fibonacci[#],Total[ IntegerDigits[ Fibonacci[ #]]]}, PrimeQ] &] (* The program uses the AllTrue function from Mathematica version 10 *)
%o (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
%Y Cf. A000045, A001605, A007953, A319230.
%K nonn,base,hard,more
%O 1,1
%A _Harvey P. Dale_, Sep 18 2018