A338824 Lexicographically earliest sequence of nonnegative integers such that for any distinct m and n, a(m) OR a(m+1) <> a(n) OR a(n+1) (where OR denotes the bitwise OR operator).

0, 0, 1, 2, 0, 4, 1, 6, 0, 8, 1, 10, 0, 12, 1, 14, 0, 16, 1, 18, 0, 20, 1, 22, 0, 24, 1, 26, 0, 28, 1, 30, 0, 32, 1, 34, 0, 36, 1, 38, 0, 40, 1, 42, 0, 44, 1, 46, 0, 48, 1, 50, 0, 52, 1, 54, 0, 56, 1, 58, 0, 60, 1, 62, 0, 64, 1, 66, 0, 68, 1, 70, 0, 72, 1, 74

Offset

1,4

Links

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Rémy Sigrist, C program for A338824

Index entries for linear recurrences with constant coefficients, signature (0,1,0,1,0,-1).

Formula

a(2*n) = 2*n-2 for any n > 0.

a(4*n+1) = 0 for any n >= 0.

a(4*n+3) = 1 for any n >= 0.

a(n) OR a(n+1) = A116966(n-2) for any n > 1.

G.f.: x^3*(1 + 2*x - x^2 + 2*x^3)/((1 - x)^2*(1 + x)^2*(1 + x^2)). - Andrew Howroyd, Nov 18 2025

Example

The first terms, alongside a(n) OR a(n+1), are:
  n   a(n)  a(n) OR a(n+1)
  --  ----  --------------
   1     0               0
   2     0               1
   3     1               3
   4     2               2
   5     0               4
   6     4               5
   7     1               7
   8     6               6
   9     0               8
  10     8               9
  11     1              11
  12    10              10

Mathematica

Block[{a = {0, 0}, b = {0}}, Do[Block[{k = 0, m}, While[! FreeQ[b, Set[m, BitOr @@ {a[[-1]], k}]], k++]; AppendTo[a, k]; AppendTo[b, m]], {i, 3, 76}]; a] (* Michael De Vlieger, Nov 12 2020 *)

Prog

(C) // See Links section.
(PARI) a(n) = if(n%2==0, n-2, bittest(n, 1)); \\ Andrew Howroyd, Nov 18 2025

Crossrefs

Cf. A116966, A338823.

Sequence in context: A176910 A243981 A369657 * A056737 A289144 A350576

Adjacent sequences: A338821 A338822 A338823 * A338825 A338826 A338827

Keyword

nonn,base,easy

Author

Rémy Sigrist, Nov 11 2020

Status

approved