A369281 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, A091255(a(n), a(n+1)) = 1.

1, 2, 3, 4, 5, 7, 6, 11, 8, 9, 13, 10, 19, 12, 21, 15, 14, 17, 16, 23, 22, 25, 18, 31, 20, 35, 24, 37, 26, 27, 32, 29, 28, 33, 38, 39, 41, 30, 47, 34, 49, 40, 55, 36, 59, 42, 43, 44, 45, 50, 51, 52, 53, 56, 57, 61, 46, 67, 48, 69, 54, 73, 58, 79, 60, 81, 62

Offset

1,2

Comments

In other words, the polynomials over GF(2) whose coefficients are encoded in the binary expansions of two consecutive terms are coprime.

As the polynomials over GF(2) whose coefficients are encoded in the binary expansions of two consecutive integers are not necessarily coprime (see A369317-A369318), the present sequence does not equal the identity map.

This sequence is a permutation of the positive integers with inverse A369282:

- we can always extend the sequence with some term of A014580 not yet in the sequence, hence the sequence is infinite, and all terms of A014580 appear in the sequence, in ascending order,

- for any k > 0, the first term >= A014580(k) is precisely A014580(k),

- if a(n) = A014580(k) for some n and the least value not among the first n terms, say u, is less than A014580(k), then a(n+1) = u,

- and eventually every integer will appear in the sequence.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Scatterplot of the first 2500 terms.

Rémy Sigrist, PARI program.

Index entries for sequences operating on GF(2)[X]-polynomials

Index entries for sequences that are permutations of the natural numbers

Prog

(PARI) See Links section.

Crossrefs

See A369293 for a similar sequence.

Cf. A014580, A091255, A369282 (inverse), A369317-A369318.

Sequence in context: A283194 A254498 A185969 * A266637 A370496 A278505

Adjacent sequences: A369278 A369279 A369280 * A369282 A369283 A369284

Keyword

nonn,base

Author

Rémy Sigrist, Jan 18 2024

Status

approved