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%I #28 Nov 04 2022 16:02:35
%S 3,4,5,7,9,11,13,15,17,23,29,43,47,83,131,137,359,431,433,449,509,569,
%T 571,2971,4723,5387,9311,9677
%N Numbers n such that all numbers of the form Fib(n)/d + d are prime (or nonexistent), where Fib(n) is the n-th Fibonacci number and d is a nontrivial divisor of Fib(n).
%C Damir et al. conjecture that this sequence is finite.
%H Mohamed Taoufiq Damir, Bernadette Faye, Florian Luca, and Amadou Tall, <a href="http://www.emis.de/journals/INTEGERS/papers/o5/o5.Abstract.html">Fibonacci numbers with prime sums of complementary divisors</a>, Integers 14 (2014), A5.
%t f2[n_] := Module[{d = Rest[Most[Divisors[n]]]}, n/d + d]; Select[Range[3, 200], And @@ PrimeQ[f2[Fibonacci[#]]] &]
%o (PARI) is(n)=my(F=fibonacci(n)); if(n%6==0 || n%25==0 || n%56==0 || n%91==0 || n%110==0 || n%153==0 || !issquarefree(F), return(0)); fordiv(F,d,if(d>1 && d<F && !isprime(F/d+d), return(0))); 1 \\ _Charles R Greathouse IV_, Feb 04 2014
%Y Not a subsequence of A037917.
%Y Cf. A001605, A080715, A233515.
%K nonn,more
%O 1,1
%A _T. D. Noe_, Jan 31 2014
%E a(18)-a(24) from _Charles R Greathouse IV_, Feb 04 2014
%E Terms 2971 to 9677 from Don Reble. - _N. J. A. Sloane_, Nov 04 2022