A059939 a(n) = floor(log_2(n+1) - 1).

0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 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, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset: 1

Author

Henry Bottomley, Feb 14 2001

Keywords

• easy
• nonn

Examples

			a(6) = floor(log_2(7) - 1) = floor(1.807...) = 1;
a(7) = floor(log_2(8) - 1) = floor(2) = 2;
a(8) = floor(log_2(9) - 1) = floor(2.169...) = 2.
		

References

• Y. S. Song, On the combinatorics of rooted binary phylogenetic trees, Annals of Combinatorics, 7, 2003, 365-379.

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1024

Programs

Mathematica

Table[Floor[Log[2,n+1]-1],{n,110}] (* Harvey P. Dale, Oct 04 2014 *)

PARI

{ a=0; p=4; for (n=1, 1024, if (n + 1 == p, a++; p*=2;); write("b059939.txt", n, " ", a); ) } \\ Harry J. Smith, Jun 30 2009

Formula

a(n) = A000523(n+1) - 1 = floor(log_10(A007931(n))).