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A282756
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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.
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0
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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F(1,3) = 2 > 1^1;
F(2,6) = 70 > 2^6 = 64;
F(3,14) = 5097243 > 3^14 = 4782969;
...
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MATHEMATICA
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f[k_, n_] := Fibonacci[n, k]
Do[Do[If[f[k, n] > k^n, {Print[{k, n}], Break[]}], {n, 0, 10000}], {k, 50}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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