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A275774 Numbers m with the property that, when a and b are positive integers such that a*b = m, |a-b| is a Fibonacci number. 0
1, 2, 3, 6, 14, 35, 611, 3524579 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is of the form Fibonacci(k) + 1. Is this sequence finite?

There are probably no more terms. If a(9) exists, it is greater than 10^200. - Charles R Greathouse IV, Aug 08 2016

LINKS

Table of n, a(n) for n=1..8.

EXAMPLE

35 is in the sequence because A038548(35) = 2 => two decompositions of 35 = 1*35 = 5*7 => 35-1 = 34 and 7-2 = 5 are Fibonacci numbers.

MATHEMATICA

Do[ds=Divisors[n]; If[EvenQ[Length[ds]], ok=True; k=1; While[k<=Length[ds]/2&&(ok=IntegerQ[Sqrt[5*(ds[[k]]-ds[[-k]])^2+4]]||IntegerQ[Sqrt[5*(ds[[k]]-ds[[-k]])^2-4]]), k++]; If[ok, Print[n]]], {n, 2, 10^7}]

PROG

(PARI) isFibonacci(n)=my(k=n^2); k+=((k+1)<<2); issquare(k)||(n>0&&issquare(k-8))

is(n)=fordiv(n, d, if(!isFibonacci(abs(n/d-d)), return(0))); 1 \\ Charles R Greathouse IV, Aug 08 2016

CROSSREFS

Cf. A000045, A038548.

Sequence in context: A093467 A246640 A080408 * A319323 A341630 A001420

Adjacent sequences:  A275771 A275772 A275773 * A275775 A275776 A275777

KEYWORD

nonn

AUTHOR

Michel Lagneau, Aug 08 2016

EXTENSIONS

a(1) inserted by Charles R Greathouse IV, Aug 08 2016

STATUS

approved

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Last modified April 22 19:11 EDT 2021. Contains 343177 sequences. (Running on oeis4.)