A000195 a(n) = floor(log(n)).

0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Equals A004233(n) - 1 for n > 1.

Does not satisfy Benford's law [Whyman et al., 2016] - N. J. A. Sloane, Feb 12 2017

Links

• T. D. Noe, Table of n, a(n) for n=1..10000
• G. Whyman, N. Ohtori, E. Shulzinger, and Ed. Bormashenko, Revisiting the Benford law: When the Benford-like distribution of leading digits in sets of numerical data is expectable?, Physica A: Statistical Mechanics and its Applications, 461, 595-601 (2016).
• Index entries for sequences related to Benford's law

Crossrefs

Cf. A000193 (nearest integer to log(n)), A004233.

Cf. A000523.

Programs

Haskell

a000195 = floor . log . fromIntegral  -- Reinhard Zumkeller, Mar 17 2015

Maple

Digits := 100; f := n->floor(evalf(log(n))); [ seq(f(n), n=1..100) ];

Mathematica

Floor@ Log@ Range@ 105 (* Michael De Vlieger, Aug 21 2017 *)

PARI

a(n)=floor(log(n))

Formula

Conjecture: a(n) = floor(3*n^2*(n^(1/(3*n^2))-1)), checked for n <= 10^6. - Joseph M. Shunia, Aug 02 2024