A105025 - OEIS

A105025

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 downward direction and convert to decimal.

0, 1, 3, 2, 4, 7, 6, 5, 11, 10, 9, 12, 15, 14, 13, 8, 18, 17, 20, 23, 22, 21, 16, 27, 26, 25, 28, 31, 30, 29, 24, 19, 33, 36, 39, 38, 37, 32, 43, 42, 41, 44, 47, 46, 45, 40, 35, 50, 49, 52, 55, 54, 53, 48, 59, 58, 57, 60, 63, 62, 61, 56, 51, 34, 68, 71, 70, 69, 64, 75, 74, 73, 76

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OFFSET

0,3

COMMENTS

This is a permutation of the nonnegative integers.

a(A214433(n)) = A105027(A214433(n)); a(A214489(n)) = A105029(A214489(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].

Index entries for sequences that are permutations of the natural numbers

Index entries for sequences related to binary expansion of n

EXAMPLE

........0

........1

.......10

.......11

......100 <- Starting here, the downward diagonals

......101 read 100, 111, 110, 101, giving the block 4, 7, 6, 5.

......110

......111

.....1000

.....1001

.....1010

.....1011

.........

MAPLE

a:=proc(i, j) if j=1 and i<=16 then 0 else convert(i+15, base, 2)[7-j] fi end: seq(a(i, 2)*2^4+a(i+1, 3)*2^3+a(i+2, 4)*2^2+a(i+3, 5)*2+a(i+4, 6), i=1..16); # this is a Maple program (not necessarily the simplest) only for one block of (2^4) numbers # Emeric Deutsch, Apr 16 2005

MATHEMATICA

numberOfBlocks = 7; bloc[n_] := Join[ Table[ IntegerDigits[k, 2], {k, 2^(n-1), 2^n-1}], Table[ Rest @ IntegerDigits[k, 2], {k, 2^n, 2^n+n}]]; Join[{0, 1}, Flatten[ Table[ Table[ Diagonal[bloc[n], k] // FromDigits[#, 2]&, {k, 0, -2^(n-1)+1, -1}], {n, 2, numberOfBlocks}]]] (* Jean-François Alcover, Nov 03 2016 *)

PROG

(Haskell)

import Data.Bits ((.|.), (.&.))

a105025 n = foldl (.|.) 0 $ zipWith (.&.)

a000079_list $ reverse $ enumFromTo n (n - 1 + a070939 n)

-- Reinhard Zumkeller, Jul 21 2012

CROSSREFS

Cf. A102370, A105026.

Cf. A070939, A000079.

Cf. A105271 (fixed points), A214416 (inverse).

Sequence in context: A261147 A212952 A246259 * A129594 A214416 A170950

Adjacent sequences: A105022 A105023 A105024 * A105026 A105027 A105028