A282756 Let F(k,n) = k*F(k,n-1) + F(k,n-2) with initial conditions F(k,0) = 0, F(k,1) = 1. Sequence lists the minimum 'n' such that F(k,n) > k^n.

3, 6, 14, 27, 45, 70, 101, 139, 184, 236, 296, 364, 440, 524, 616, 716, 826, 943, 1070, 1205, 1350, 1503, 1666, 1838, 2019, 2210, 2410, 2620, 2839, 3069, 3308, 3557, 3815, 4084, 4363, 4652, 4951, 5261, 5580, 5910, 6251, 6601, 6963, 7334, 7717, 8110, 8513, 8928, 9353, 9788

Offset: 1

Author

Sergio Falcon, Feb 21 2017

Keywords

• nonn

Examples

			F(1,3) = 2 > 1^1;
F(2,6) = 70 > 2^6 = 64;
F(3,14) = 5097243 > 3^14 = 4782969;
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Links

• Sergio Falcón and Ángel Plaza, On the Fibonacci k-numbers, Chaos, Solitons and Fractals, Elsevier, 32 (5), 1615 - 1624, 2007.

Crossrefs

Cf. A000045, A000129, A006190.

Programs

Mathematica

f[k_, n_] := Fibonacci[n, k]
Do[Do[If[f[k, n] > k^n, {Print[{k, n}], Break[]}], {n, 0, 10000}], {k, 50}]