A369302 -id:A369302 - cp's OEIS frontend

A369293 Lexicographically earliest sequence of distinct positive integers such that a(1) = 1, a(2) = 2, and for any n > 1, A091255(a(n), a(n+1)) <> 1.

1, 2, 4, 6, 3, 5, 9, 7, 14, 8, 10, 12, 15, 17, 18, 16, 20, 22, 11, 29, 23, 13, 26, 24, 27, 21, 28, 30, 32, 34, 33, 31, 62, 36, 35, 42, 38, 19, 53, 39, 40, 43, 25, 50, 44, 46, 45, 48, 51, 54, 49, 56, 52, 57, 58, 60, 63, 65, 66, 64, 68, 70, 72, 71, 61, 122, 74

Offset: 1

Rémy Sigrist, Jan 18 2024

In other words, the polynomials over GF(2) whose coefficients are encoded in the binary expansions of two consecutive terms (beyond the initial term) are not coprime.
This sequence is a variant of the EKG sequence (A064413).
Is this a permutation of the positive integers?

			The first terms, alongside A091255(a(n), a(n+1)), are:
  n   a(n)  A091255(a(n), a(n+1))
  --  ----  ---------------------
   1     1                      1
   2     2                      2
   3     4                      2
   4     6                      3
   5     3                      3
   6     5                      3
   7     9                      7
   8     7                      7
   9    14                      2
  10     8                      2

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Scatterplot of the first 100000 terms
Rémy Sigrist, PARI program
Index entries for sequences operating on GF(2)[X]-polynomials
Index entries for sequences related to EKG sequence

See A369281 and A369294 for similar sequences.

Cf. A064413, A091255, A369302.

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A369293 Lexicographically earliest sequence of distinct positive integers such that a(1) = 1, a(2) = 2, and for any n > 1, A091255(a(n), a(n+1)) <> 1.

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