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

Author

Rémy Sigrist, Nov 11 2020

Keywords

• nonn
• base

Examples

			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
		

Links

• Rémy Sigrist, C program for A338824

Crossrefs

Cf. A116966, A338823.

Programs

C

See Links section.

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 *)

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.