A338824 -id:A338824 - cp's OEIS frontend

A338823 Lexicographically earliest sequence of positive 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).

1, 1, 2, 2, 4, 1, 6, 8, 1, 10, 2, 13, 1, 16, 2, 17, 4, 4, 8, 8, 16, 4, 18, 5, 24, 1, 26, 2, 28, 3, 32, 1, 36, 2, 32, 4, 24, 32, 7, 40, 1, 42, 2, 44, 1, 48, 2, 49, 4, 40, 8, 49, 6, 48, 4, 56, 2, 57, 4, 58, 5, 64, 1, 66, 2, 68, 3, 72, 1, 76, 2, 72, 4, 64, 8, 71

Offset: 1

Rémy Sigrist, Nov 11 2020

			The first terms, alongside a(n) OR a(n+1), are:
  n   a(n)  a(n) OR a(n+1)
  --  ----  --------------
   1     1               1
   2     1               3
   3     2               2
   4     2               6
   5     4               5
   6     1               7
   7     6              14
   8     8               9
   9     1              11
  10    10              10
  11     2              15
  12    13              13

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Colored scatterplot of the first 10000 terms (where the color is function of the parity of n)
Rémy Sigrist, C program for A338823

Cf. A088177, A338824.

C
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See Links section.
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Block[{a = {1, 1}, b = {1}}, Do[Block[{k = 1, 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 *)

A355413 Lexicographically earliest infinite sequence of positive numbers such that, for n>1, a(n) AND a(n-1) is distinct from all previous AND operations between adjacent terms, where AND is the binary AND operator.

Original entry on oeis.org

0, 1, 3, 3, 6, 5, 7, 7, 14, 9, 11, 11, 14, 13, 15, 15, 30, 17, 19, 19, 22, 21, 23, 23, 30, 25, 27, 27, 30, 29, 31, 31, 62, 33, 35, 35, 38, 37, 39, 39, 46, 41, 43, 43, 46, 45, 47, 47, 62, 49, 51, 51, 54, 53, 55, 55, 62, 57, 59, 59, 62, 61, 63, 63, 126, 65, 67, 67, 70, 69, 71, 71, 78, 73, 75, 75

Offset: 0

Scott R. Shannon, Jul 01 2022

Each term must be chosen so that a subsequent term can always been found. This implies, for example, no power of 2 can ever be a term as the result of an AND operation between such a number and any following number will be either 0 or the power of 2, both of which have already appeared as the result of AND operations.

Every a(n) where n is odd is a fixed point.

			a(3) = 3 as a(2) = 3 and 3 AND 3 = 3, which has not occurred earlier for any AND's between adjacent terms. Note that a(3) cannot equal 2 = 10_2 as the result of any subsequent AND operation with 2 would be 0 or 2, both of which have already occurred.

Scott R. Shannon, Line graph of the first 100000 terms.

Cf. A007088, A129760, A338824.

cp's OEIS Frontend

A338823 Lexicographically earliest sequence of positive 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).

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