|
Search: id:A103354
|
|
|
| A103354 |
|
Floor(x), where x is the solution to x = 2^(n-x). |
|
+0
6
|
|
| 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; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
Partial sums seem to be A006697(n-1) = A094913(n-1)+1. - M. F. Hasler, Dec 14 2007
|
|
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
|
|
PROGRAM
|
(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
|
Cf. A006697 (partial sums), A094913.
Sequence in context: A049472 A125229 A122797 this_sequence A127038 A051068 A050294
Adjacent sequences: A103351 A103352 A103353 this_sequence A103355 A103356 A103357
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Mar 21 2005
|
|
EXTENSIONS
|
Edited by M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Dec 14 2007
|
|
|
Search completed in 0.002 seconds
|
