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A103354
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a(n) = floor(x), where x is the solution to x = 2^(n-x).
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9
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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
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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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
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MAPLE
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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:
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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