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Prime-indexed primes p such that Fibonacci(p) is prime.
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%I #69 Nov 19 2024 06:34:20

%S 3,5,11,17,83,431,509,130021,148091,433781

%N Prime-indexed primes p such that Fibonacci(p) is prime.

%C Intersection of A006450 and A083668. - _Michel Marcus_, Oct 21 2016

%F a(n) = prime(A277575(n)).

%F a(n) = prime(prime(A122534(n))).

%e 17 = A000040(7), with 7 itself being a prime, and A000045(17) = 1597, a prime, thus 17 is included in this sequence.

%t Select[Prime[Prime[Range[37000]]],PrimeQ[Fibonacci[#]]&] (* _Harvey P. Dale_, Sep 12 2019 *)

%o (PARI) isok(p) = isprime(p) && isprime(primepi(p)) && isprime(fibonacci(p)); \\ _Michel Marcus_, Oct 21 2016

%Y Cf. A000040, A000045, A006450, A083668, A122534, A277575.

%K nonn,hard,more

%O 1,1

%A _Bobby Jacobs_, Oct 21 2016