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%I #12 Feb 20 2023 07:51:51
%S 2,1,3,2,3,5,1,6,4,3,5,2,5,3,4,5,6,10,18,1,11,8,6,5,4,7,10,3,5,7,9,15,
%T 2,11,7,5,8,14,3,10,7,4,9,5,11,6,7,8,10,12,15,21,34,1,40,24,17,13,11,
%U 10,8,7,13,6,11,5,14,9,17,4,11,7,10,13,22,3,17
%N Least integer k such that floor(k*log(n+1))>k*log(n).
%C Equivalently, a(n) is the least integer k for which there is an integer J such that n^k < e^J < (n+1)^k; or, equivalently, such that there is a rational number H with denominator k for which log(n) < H < log(n+1).
%t Table[k=1; While[Floor[k*Log[n+1]] <= k*Log[n], k++]; k, {n, 100}]
%o (Sage) A183163 = lambda n: next(k for k in IntegerRange(1, infinity) if floor(k*log(n+1)) > k*log(n)) # _D. S. McNeil_, Dec 28 2010
%Y Cf. A183162.
%K nonn
%O 1,1
%A _Clark Kimberling_, Dec 27 2010
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