A233514 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).

3, 4, 5, 7, 9, 11, 13, 15, 17, 23, 29, 43, 47, 83, 131, 137, 359, 431, 433, 449, 509, 569, 571, 2971, 4723, 5387, 9311, 9677

Offset: 1

Author

T. D. Noe, Jan 31 2014

Keywords

• nonn
• more

Comments

Damir et al. conjecture that this sequence is finite.

Links

• Mohamed Taoufiq Damir, Bernadette Faye, Florian Luca, and Amadou Tall, Fibonacci numbers with prime sums of complementary divisors, Integers 14 (2014), A5.

Crossrefs

Not a subsequence of A037917.

Cf. A001605, A080715, A233515.

Programs

Mathematica

f2[n_] := Module[{d = Rest[Most[Divisors[n]]]}, n/d + d]; Select[Range[3, 200], And @@ PrimeQ[f2[Fibonacci[#]]] &]

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 && dCharles R Greathouse IV, Feb 04 2014

Extensions

a(18)-a(24) from Charles R Greathouse IV, Feb 04 2014

Terms 2971 to 9677 from Don Reble. - N. J. A. Sloane, Nov 04 2022