A102572 a(n) = floor(log_4(n)).

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

Offset: 1

Author

N. J. A. Sloane, Dec 23 2006

Keywords

• nonn

Crossrefs

Cf. A000523, A062153.

Programs

Magma

[ Ilog(4,n) : n in [1..150] ];

PARI

a(n)=#digits(n,4)-1 \\ Twice as fast as a(n)=for(i=0,n,(n>>=2)||return(i)); the naïve code a(n)=log(n)\log(4) works for standard realprecision=28 only up to n=4^47-5 and it is slower by another factor 2. - M. F. Hasler, Mar 11 2015

PARI

A102572(n)=logint(n,4) \\ M. F. Hasler, Nov 07 2019

Formula

G.f.: (1/(1 - x))*Sum_{k>=1} x^(4^k). - Ilya Gutkovskiy, Jan 08 2017