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%I #11 Jan 03 2016 13:37:00
%S 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,
%T 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,
%U 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
%N a(n) = floor(log_2(n+1) - 1).
%D Y. S. Song, On the combinatorics of rooted binary phylogenetic trees, Annals of Combinatorics, 7, 2003, 365-379.
%H Harry J. Smith, <a href="/A059939/b059939.txt">Table of n, a(n) for n = 1..1024</a>
%F a(n) = A000523(n+1) - 1 = floor(log_10(A007931(n))).
%e a(6) = floor(log_2(7) - 1) = floor(1.807...) = 1;
%e a(7) = floor(log_2(8) - 1) = floor(2) = 2;
%e a(8) = floor(log_2(9) - 1) = floor(2.169...) = 2.
%t Table[Floor[Log[2,n+1]-1],{n,110}] (* _Harvey P. Dale_, Oct 04 2014 *)
%o (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
%K easy,nonn
%O 1,7
%A _Henry Bottomley_, Feb 14 2001
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