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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.
1
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
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
KEYWORD
nonn,base,hard,more
AUTHOR
Harvey P. Dale, Sep 18 2018
STATUS
approved