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 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). 1
 3, 4, 5, 7, 9, 11, 13, 15, 17, 23, 29, 43, 47, 83, 131, 137, 359, 431, 433, 449, 509, 569, 571 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Damir et al. conjecture that this sequence is finite. Note that it is A001605 (indices of prime Fibonacci numbers) and two additional terms (9 and 15) so far. Below 3000 the remaining candidates are 1373, 1543, 1741, 1801, 2141, 2143, 2269, 2309, 2339, 2393, 2543, 2591, 2593, 2711, 2749, 2969, and 2971. Probably only the last is in the sequence. - Charles R Greathouse IV, Feb 04 2014 LINKS 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

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Last modified March 19 13:22 EDT 2019. Contains 321330 sequences. (Running on oeis4.)