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A103354
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Floor(x), where x is the solution to x = 2^(n-x).
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7
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1, 1, 2, 2, 3, 4, 4, 5, 6, 7, 8, 8, 9, 10, 11, 12, 13, 14, 15, 16, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 64, 65, 66, 67
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Partial sums seem to be A006697(n-1) = A094913(n-1)+1. - M. F. Hasler, Dec 14 2007
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FORMULA
| a(n) is approximately n/(1+log_2(n)/n).
a(n) = [ LambertW(log(2)*2^n)/log(2) ] = [ n - log_2(n) + log_2(n)/(n log(2)) + O((log(n)/n)^2) ] = [ n - log_2(n) + 1.5*log_2(n)/n ] at least for all n<10^7. - M. F. Hasler, Dec 14 2007
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MATHEMATICA
| a[n_] := Floor[ FullSimplify[ ProductLog[ 2^n*Log[2]]/Log[2]]]; Table[a[n], {n, 1, 74}] (* From Jean-François Alcover, Dec 13 2011, after M. F. Hasler *)
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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
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CROSSREFS
| Cf. A006697 (partial sums), A094913.
Sequence in context: A049472 A125229 A122797 * A127038 A175268 A051068
Adjacent sequences: A103351 A103352 A103353 * A103355 A103356 A103357
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mar 21 2005
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EXTENSIONS
| Edited by M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Dec 14 2007
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