

A105027


Write numbers in binary under each other; to get the next block of 2^k (k >= 0) terms of the sequence, start at 2^k, read diagonals in upward direction and convert to decimal.


12



0, 1, 3, 2, 6, 5, 4, 7, 15, 10, 9, 8, 11, 14, 13, 12, 28, 23, 18, 17, 16, 19, 22, 21, 20, 31, 26, 25, 24, 27, 30, 29, 61, 44, 39, 34, 33, 32, 35, 38, 37, 36, 47, 42, 41, 40, 43, 46, 45, 60, 55, 50, 49, 48, 51, 54, 53, 52, 63, 58, 57, 56, 59, 62, 126, 93, 76, 71, 66, 65, 64, 67, 70
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OFFSET

0,3


COMMENTS

This is a permutation of the nonnegative integers.
Structure: blocks of size 2^k  1 taken from A102370, interspersed with terms of A102371.  Philippe Deléham, Nov 17 2007
a(A062289(n)) = A102370(n) for n > 0; a(A000225(n)) = A102371(n); a(A214433(n)) = A105025(a(n)).  Reinhard Zumkeller, Jul 21 2012


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].
David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.
Index entries for sequences that are permutations of the natural numbers
Index entries for sequences related to binary expansion of n


FORMULA

a(2^n  1) = A102371(n) for n > 0.  Philippe Deléham, May 10 2005


EXAMPLE

........0
........1
.......10
.......11
......100 < Starting here, the upward diagonals
......101 read 110, 101, 100, 111, giving the block 6, 5, 4, 7.
......110
......111
.....1000
.....1001
.....1010
.....1011
.........


MATHEMATICA

block[k_] := Module[{t}, t = Table[PadLeft[IntegerDigits[n, 2], k+1], {n, 2^(k1), 2^(k+1)1}]; Table[FromDigits[Table[t[[nm+1, m]], {m, 1, k+1}], 2], {n, 2^(k1)+1, 2^(k1)+2^k}]]; block[0] = {0, 1}; Table[block[k], {k, 0, 6}] // Flatten (* JeanFrançois Alcover, Jun 30 2015 *)


PROG

(Haskell)
import Data.Bits ((..), (.&.))
a105027 n = foldl (..) 0 $ zipWith (.&.)
a000079_list $ enumFromTo (n + 1  a070939 n) n
 Reinhard Zumkeller, Jul 21 2012


CROSSREFS

Cf. A102370, A105025, A105026, A105028.
Cf. A070939, A000079.
Cf. A214414 (fixed points), A214417 (inverse).
Sequence in context: A058401 A244426 A214417 * A234024 A194861 A194840
Adjacent sequences: A105024 A105025 A105026 * A105028 A105029 A105030


KEYWORD

nonn,nice,base,changed


AUTHOR

N. J. A. Sloane, Apr 03 2005


EXTENSIONS

More terms from John W. Layman, Apr 07 2005


STATUS

approved



