

A064414


Fix a > 0, b > 0, k > 0 and define G_1 = a, G_2 = b, G_k = G_(k1) + G_(k2); 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
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OFFSET

1,2


COMMENTS

The squares of this sequence are the squares in A232656.
Conjecture: these are the numbers j such that j^2 = Sum_{dj} phi(d)*A001177(d), where phi = Euler's totient function (A000010). See A232656. (End)


REFERENCES

Teruo Nishiyama, Fibonacci numbers, SuuriKagaku, No. 285, March 1987, 6769, (in Japanese).


LINKS



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[k2]*a + Fibonacci[k1]*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]] (* JeanFrançois Alcover, Jul 19 2012 *)


CROSSREFS



KEYWORD

easy,nonn,nice


AUTHOR



EXTENSIONS



STATUS

approved



