|
| |
|
|
A004755
|
|
Binary expansion starts 11.
|
|
10
| |
|
|
3, 6, 7, 12, 13, 14, 15, 24, 25, 26, 27, 28, 29, 30, 31, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| a(n) is the smallest value > a(n-1) (or > 1 for n=1) for which A001511(a(n)) = A001511(n). - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Oct 23 2006
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=1..1023
R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
|
|
|
FORMULA
| a(2n) = 2a(n), a(2n+1) = 2a(n) + 1 + 2[n==0].
a(n) = n + 2 * 2^floor(log2(n)) = A004754(n) + A053644(n).
a(n) = 2n + A080079(n); - Benoit Cloitre, Feb 22 2003
G.f. 1/(1+x) * (1 + sum(k>=0, 2^k(2t+t^2)/(1+t), t=x^2^k)).
a(n) = n + 2^{floor(log_2(n))+1} = n + A062383(n). - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Oct 23 2006
|
|
|
EXAMPLE
| 12 in binary is 1100, so 12 is in sequence.
|
|
|
PROG
| (PARI) a(n)=n+2*2^floor(log(n)/log(2))
|
|
|
CROSSREFS
| Equals union of A079946 and A080565.
Cf. A004754 (10), A004756 (100), A004757 (101), A004758 (110), A004759 (111).
Cf. A004760, A053644, A062050, A076877.
Sequence in context: A028802 A141742 * A004760 A186083 A093906 A152829
Adjacent sequences: A004752 A004753 A004754 * A004756 A004757 A004758
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| Edited by Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 12 2003
|
| |
|
|
