A183163 Least integer k such that floor(k*log(n+1))>k*log(n).

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, 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, 10, 8, 7, 13, 6, 11, 5, 14, 9, 17, 4, 11, 7, 10, 13, 22, 3, 17

Offset: 1

Author

Clark Kimberling, Dec 27 2010

Keywords

• nonn

Comments

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).

Crossrefs

Cf. A183162.

Programs

Mathematica

Table[k=1; While[Floor[k*Log[n+1]] <= k*Log[n], k++]; k, {n, 100}]

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