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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.

%I A282756 #24 Sep 09 2017 03:32:21
%S A282756 3,6,14,27,45,70,101,139,184,236,296,364,440,524,616,716,826,943,1070,
%T A282756 1205,1350,1503,1666,1838,2019,2210,2410,2620,2839,3069,3308,3557,
%U A282756 3815,4084,4363,4652,4951,5261,5580,5910,6251,6601,6963,7334,7717,8110,8513,8928,9353,9788
%N 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.
%H A282756 Sergio Falcón and Ángel Plaza, <a href="http://dx.doi.org/10.1016/j.chaos.2006.09.022">On the Fibonacci k-numbers</a>, Chaos, Solitons and Fractals, Elsevier, 32 (5), 1615 - 1624, 2007.
%e A282756 F(1,3) = 2 > 1^1;
%e A282756 F(2,6) = 70 > 2^6 = 64;
%e A282756 F(3,14) = 5097243 > 3^14 = 4782969;
%e A282756 ...
%t A282756 f[k_, n_] := Fibonacci[n, k]
%t A282756 Do[Do[If[f[k, n] > k^n, {Print[{k, n}], Break[]}], {n, 0, 10000}], {k, 50}]
%Y A282756 Cf. A000045, A000129, A006190.
%K A282756 nonn
%O A282756 1,1
%A A282756 _Sergio Falcon_, Feb 21 2017