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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

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 A193339 A049646

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

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