|
Search: id:A106623
|
|
|
| A106623 |
|
Write numbers 0, 1, 2, ... in binary under each other, right-adjusted; shift the 2^k's column upwards by prime(k+1) places (for k >= 0); read the resulting array across rows starting at the (old) zero row; convert to decimal. |
|
+0
1
|
|
| 6, 13, 12, 11, 10, 25, 24, 31, 30, 21, 20, 19, 18, 17, 16, 23, 22, 29, 28, 59, 58, 41, 40, 47, 46, 37, 36, 35, 34, 33, 32, 39, 38, 45, 44, 43, 42, 57, 56, 63, 62, 53, 52, 51, 50, 49, 48, 119, 118, 125, 124, 91, 90, 73, 72, 79, 78, 69, 68, 67, 66, 65, 64, 71, 70, 77, 76, 75, 74
(list; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
LINKS
|
David Applegate, Benoit Cloitre, Philippe DELEHAM and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].
|
|
FORMULA
|
a(n) = Sum_{k >= 0} 2^k*(1-(-1)^floor((n+prime(k+1))/2^k))/2.
|
|
EXAMPLE
|
The array before the columns are shifted upwards:
--------- <- the "zero" line
....00000
....00001
....00010
....00011
....00100
....00101
....00110
....00111
....01000
.........
After the upwards shifts:
....0
....0
....0
....0
....00
....00
....000
....000
....0000
....00000
....00111
--------- <- the "zero" line
....00110 = 6
....01101 = 13
....01100 = 12
....01011 = 11
....01010 = 10
....11001 = 25
....11000 = 24
....11111 = 31
....11110 = 30
.........
|
|
PROGRAM
|
(PARI) {a(n) = local(s, m, k); s=0; k=0; while(1, m=floor((n+prime(k+1))/2^k); if(m==0, return(s)); if(m%2, s+=2^k); k++)} (Alekseyev)
|
|
CROSSREFS
|
Cf. A102370.
Sequence in context: A070396 A130012 A090324 this_sequence A115010 A066826 A031113
Adjacent sequences: A106620 A106621 A106622 this_sequence A106624 A106625 A106626
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com) and Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Feb 13 2005
|
|
EXTENSIONS
|
More terms from Max Alekseyev (maxale(AT)gmail.com), May 17 2005
|
|
|
Search completed in 0.002 seconds
|
