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

1,7

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

Formula

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Sequence in context: A345378 A071840 A000193 * A071842 A344517 A371355

Adjacent sequences: A059936 A059937 A059938 * A059940 A059941 A059942

Keyword

easy,nonn

Author

Henry Bottomley, Feb 14 2001

Status

approved