

A233514


Numbers n such that all numbers of the form Fib(n)/d + d are prime (or nonexistent), where Fib(n) is the nth 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
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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

Table of n, a(n) for n=1..23.
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

Subsequence of A037917.
Cf. A001605, A080715, A233515.
Sequence in context: A284752 A161153 A128201 * A096262 A308168 A193339
Adjacent sequences: A233511 A233512 A233513 * A233515 A233516 A233517


KEYWORD

nonn,hard


AUTHOR

T. D. Noe, Jan 31 2014


EXTENSIONS

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


STATUS

approved



