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

1,2

Comments

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?

Links

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

Example

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

Prog

(PARI) See Links section.

Crossrefs

See A369281 and A369294 for similar sequences.

Cf. A064413, A091255, A369302.

Sequence in context: A373546 A175213 A346150 * A104492 A331522 A075075

Adjacent sequences: A369290 A369291 A369292 * A369294 A369295 A369296

Keyword

nonn,base

Author

Rémy Sigrist, Jan 18 2024

Status

approved