A083668 - OEIS

%I #33 Oct 21 2016 11:06:53

%S 3,5,7,11,13,17,23,29,43,47,83,131,137,359,431,433,449,509,569,571,

%T 2971,4723,5387,9311,9677,14431,25561,30757,35999,37511,50833,81839,

%U 104911,130021,148091,201107,397379,433781,590041,593689,604711,931517,1049897,1285607,1636007,1803059,1968721

%N Prime indices of prime Fibonacci numbers.

%C Same as A001605 without the number 4.

%C From _V. Raman_, Oct 04 2012: (Start)

%C Also the indices of prime Fibonacci numbers which can be written as the sum of two positive squares.

%C The Fibonacci numbers F(6k+1) and F(6k+5) are congruent to 1 (mod 4).

%C (End)

%e For Fib(n) to be prime, n must be prime, except for n=4. The first 9 primes are: 2, 3, 5, 7, 11, 13, 17, 19 and 23. The corresponding Fibonacci numbers are: 1, 2, 5, 13, 89, 233, 1597, 4181 and 28657. All of these are prime except Fib(2) = 1 and Fib(19) = 4181. So the first 7 terms of this sequence are 3, 5, 7, 11, 13, 17 and 23.

%t Do[ If[ PrimeQ[ Fibonacci[ Prime[n]]], Print[ Prime[n]]], {n, 1, 1000}]

%o (PARI) pif(n) = { forprime(x=2,n, if(isprime(fibonacci(x)), print1(x" "))) }

%o (PARI) is(p)=isprime(p) & ispseudoprime(fibonacci(p))  \\ _Charles R Greathouse IV_, Sep 19 2012

%Y Cf. A001605, A075737.

%K nonn

%O 1,1

%A _Cino Hilliard_, Jun 14 2003

%E More terms from _Zak Seidov_, Aug 31 2006

%E Replaced the erroneous example _Harry J. Smith_, Jan 16 2009

%E Terms a(42) to a(47) added by _V. Raman_, Oct 04 2012

%E Definition and wrong statement in example corrected by _M. F. Hasler_, Oct 08 2012