|
| |
|
|
A006520
|
|
Partial sums of A006519.
(Formerly M2344)
|
|
5
|
|
|
|
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;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
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. [Jonathan Vos Post, Feb 18 2010]
|
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
|
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
V. Meally, Letter to N. J. A. Sloane, May 1975
R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
|
|
|
FORMULA
|
a(n)/(n*log(n)) is bounded. - Benoit Cloitre, 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, Apr 17 2003
a(n) = b(n+1), with b(2n) = 2b(n) + n, b(2n+1) = 2b(n) + n + 1. - Ralf Stephan, Sep 07 2003
|
|
|
MATHEMATICA
|
Table[ 2^IntegerExponent[n, 2], {n, 1, 70}] // Accumulate (* Jean-François Alcover, May 14 2013 *)
|
|
|
PROG
|
(PARI) a(n)=sum(i=1, n, 2^valuation(i, 2))
|
|
|
CROSSREFS
|
First differences of A022560.
Sequence in context: A047460 A193532 A068056 * A054204 A050003 A285033
Adjacent sequences: A006517 A006518 A006519 * A006521 A006522 A006523
|
|
|
KEYWORD
|
nonn,easy,changed
|
|
|
AUTHOR
|
N. J. A. Sloane, Simon Plouffe
|
|
|
EXTENSIONS
|
More terms from Benoit Cloitre, Dec 17 2002
|
|
|
STATUS
|
approved
|
| |
|
|
