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

1,1

Comments

Damir et al. conjecture that this sequence is finite.

Links

Table of n, a(n) for n=1..28.

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

Mathematica

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

Prog

(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

Crossrefs

Not a subsequence of A037917.

Cf. A001605, A080715, A233515.

Sequence in context: A161153 A128201 A347301 * A096262 A308168 A193339

Adjacent sequences: A233511 A233512 A233513 * A233515 A233516 A233517

Keyword

nonn,more

Author

T. D. Noe, Jan 31 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

Status

approved