|
|
A059939
|
|
a(n) = floor(log_2(n+1) - 1).
|
|
3
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,7
|
|
REFERENCES
|
Y. S. Song, On the combinatorics of rooted binary phylogenetic trees, Annals of Combinatorics, 7, 2003, 365-379.
|
|
LINKS
|
|
|
FORMULA
|
|
|
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
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|