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A006520
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Partial sums of A006519.
(Formerly M2344)
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3
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1, 3, 4, 8, 9, 11, 12, 20, 21, 23, 24, 28, 29, 31, 32, 48, 49, 51, 52, 56, 57, 59, 60, 68, 69, 71, 72, 76, 77, 79, 80, 112, 113, 115, 116, 120, 121, 123, 124, 132, 133, 135, 136, 140, 141, 143, 144, 160, 161, 163, 164, 168, 169, 171, 172, 180, 181, 183, 184, 188, 189
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The subsequence of primes in this partial sum begins: 3, 11, 23, 29, 31, 59, 71, 79, 113, 163, 181. The subsequence of powers in this partial sum begins: 1, 4, 8, 9, 32, 49, 121, 144, 169. [From Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 18 2010]
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
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FORMULA
| a(n)/(n*log(n)) is bounded - Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 17 2002
G.f.: 1/x/(1-x) * (x/(1-x) + Sum(k>=1, 2^(k-1)*x^2^k/(1-x^2^k))). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Apr 17 2003
a(n) = b(n+1), with b(2n) = 2b(n) + n, b(2n+1) = 2b(n) + n + 1. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 07 2003
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PROG
| (PARI) a(n)=sum(i=1, n, 2^valuation(i, 2))
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CROSSREFS
| First differences of A022560.
Sequence in context: A047460 A193532 A068056 * A054204 A050003 A073258
Adjacent sequences: A006517 A006518 A006519 * A006521 A006522 A006523
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
| More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 17 2002
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