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.

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

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^(k-1), 2^(k+1)-1}]; Table[FromDigits[Table[t[[n-m+1, m]], {m, 1, k+1}], 2], {n, 2^(k-1)+1, 2^(k-1)+2^k}]]; block[0] = {0, 1}; Table[block[k], {k, 0, 6}] // Flatten (* Jean-François 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
(PARI) apply( {A105027(n, L=exponent(n+!n))=sum(k=0, L, bitand(n+k-L, 2^k))}, [0..55]) \\ M. F. Hasler, Apr 18 2022

Crossrefs

Cf. A102370, A105025, A105026, A105028.

Cf. A070939, A000079.

Cf. A214414 (fixed points), A214417 (inverse).

Sequence in context: A244426 A214417 A377440 * A234024 A194861 A194840

Adjacent sequences: A105024 A105025 A105026 * A105028 A105029 A105030

Keyword

nonn,nice,base

Author

N. J. A. Sloane, Apr 03 2005

Extensions

More terms from John W. Layman, Apr 07 2005

Status

approved