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A064414 Fix a > 0, b > 0, k > 0 and define G_1 = a, G_2 = b, G_k = G_(k-1) + G_(k-2); sequence gives n such there exists (a, b) where G_k is divisible by n. 6
1, 2, 3, 4, 6, 7, 9, 14, 23, 27, 43, 49, 67, 81, 83, 86, 98, 103, 127, 134, 163, 167, 206, 223, 227, 243, 254, 283, 326, 343, 367, 383, 443, 446, 463, 467, 487, 503, 523, 529, 547, 566, 587, 607, 643, 647, 683, 686, 727, 729, 734, 787, 823, 827, 863, 883, 887 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Conjecture: these are the n such that n^2 = Sum_{d|n} phi(d)*A001177(d), where phi = Euler's totient function (A000010). See A232656. - Logan J. Kleinwaks, Oct 29 2017

REFERENCES

Teruo Nishiyama, Fibonacci numbers, Suuri-Kagaku, No. 285, March 1987, 67-69, (in Japanese).

LINKS

Table of n, a(n) for n=1..57.

B. Avila and T. Khovanova, Free Fibonacci Sequences, arXiv preprint arXiv:1403.4614 [math.NT], 2014 and J. Int. Seq. 17 (2014) # 14.8.5.

EXAMPLE

If a = 1, b = 4, then G_k is (1,4,5,9,14,23,....) and no G_k is a multiple of 11. Therefore 11 is not in the sequence.

MATHEMATICA

g[a_, b_, k_] := Fibonacci[k-2]*a + Fibonacci[k-1]*b; ok[n_] := Catch[ Do[ test = Catch[ Do[ If[ Divisible[g[a, b, k], n], Throw[True]], {k, 1, 2*n}]]; If[test == Null, Throw[False]], {a, 1, Floor[Sqrt[n]]}, {b, 1, Floor[Sqrt[n]]}]] ; Reap[ Do[ If[ok[n] == Null, Print[n]; Sow[n]], {n, 1, 1000}]][[2, 1]] (* Jean-Fran├žois Alcover, Jul 19 2012 *)

CROSSREFS

Prime members are in A000057.

The squares of this sequence are the squares in A232656. - Logan J. Kleinwaks, Oct 29 2017

Cf. A232357.

Sequence in context: A055494 A239115 A165773 * A224482 A002475 A208281

Adjacent sequences:  A064411 A064412 A064413 * A064415 A064416 A064417

KEYWORD

easy,nonn,nice

AUTHOR

Naohiro Nomoto, Oct 15 2001

EXTENSIONS

More terms from David Wasserman, Jul 18 2002

Name edited by David A. Corneth, Oct 30 2017

STATUS

approved

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Last modified September 19 18:47 EDT 2018. Contains 315210 sequences. (Running on oeis4.)