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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 numbers m such that there exists (a, b) where G_k is divisible by m. 7
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
From Logan J. Kleinwaks, Oct 29 2017: (Start)
The squares of this sequence are the squares in A232656.
Conjecture: these are the numbers j such that j^2 = Sum_{d|j} phi(d)*A001177(d), where phi = Euler's totient function (A000010). See A232656. (End)
REFERENCES
Teruo Nishiyama, Fibonacci numbers, Suuri-Kagaku, No. 285, March 1987, 67-69, (in Japanese).
LINKS
Brandon Avila and Tanya Khovanova, Free Fibonacci Sequences, Journal of Integer Sequences, Vol. 17 (2014), Article 14.8.5; arXiv preprint, arXiv:1403.4614 [math.NT], 2014.
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-François Alcover, Jul 19 2012 *)
CROSSREFS
Prime terms are in A000057.
Sequence in context: A055494 A239115 A165773 * A224482 A002475 A208281
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 June 21 06:38 EDT 2024. Contains 373540 sequences. (Running on oeis4.)