OFFSET
1,3
COMMENTS
Partial sums seem to be A006697(n-1) = A094913(n-1) + 1. - M. F. Hasler, Dec 14 2007 [Confirmed by Allouche and Shallit, 2016. - N. J. A. Sloane, Mar 24 2017]
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
J.-P. Allouche, J. Shallit, On the subword complexity of the fixed point of a -> aab, b -> b, and generalizations, arXiv preprint arXiv:1605.02361 [math.CO], 2016.
FORMULA
a(n) is approximately n/(1+log_2(n)/n).
a(n) = floor(LambertW(log(2)*2^n)/log(2)) = floor(n - log_2(n) + log_2(n)/(n log(2)) + O((log(n)/n)^2)) = floor(n - log_2(n) + 1.5*log_2(n)/n) at least for all n < 10^7. - M. F. Hasler, Dec 14 2007
MAPLE
A[1]:= 1;
for n from 2 to 100 do
for x from A[n-1] while x <= 2^(n-x) do od;
A[n]:= x-1;
od:
seq(A[i], i=1..100); # Robert Israel, Dec 04 2016
MATHEMATICA
a[n_] := Floor[ FullSimplify[ ProductLog[ 2^n*Log[2]]/Log[2]]]; Table[a[n], {n, 1, 74}] (* Jean-François Alcover, Dec 13 2011, after M. F. Hasler *)
PROG
(PARI) A103354(n)=floor(solve(X=1, log(n)*2, X-2^(n-X))+1e-9) \\ M. F. Hasler, Dec 14 2007
(PARI) A103354(n)=floor(n-log(n)/log(2)*(1-1.5/n)) \\ M. F. Hasler, Dec 14 2007
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 21 2005
EXTENSIONS
Edited by M. F. Hasler, Dec 14 2007
STATUS
approved