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,
- 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
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jan 18 2024
STATUS
approved