OFFSET
1,1
COMMENTS
Equivalently, numbers k such that A369317(k) <> 1.
Two consecutive integers are always coprime, however the polynomials over GF(2) whose coefficients are encoded in the binary expansions of two consecutive integers are not necessarily coprime, hence this sequence.
EXAMPLE
The first terms, alongside the correspond GF(2)[X]-polynomials, are:
n a(n) P(a(n)) P(a(n)+1) gcd(P(a(n)), P(a(n)+1))
-- ---- ------------------- ------------------- -----------------------
1 5 X^2 + 1 X^2 + X X + 1
2 9 X^3 + 1 X^3 + X X + 1
3 17 X^4 + 1 X^4 + X X + 1
4 23 X^4 + X^2 + X + 1 X^4 + X^3 X + 1
5 27 X^4 + X^3 + X + 1 X^4 + X^3 + X^2 X^2 + X + 1
6 29 X^4 + X^3 + X^2 + 1 X^4 + X^3 + X^2 + X X + 1
7 33 X^5 + 1 X^5 + X X + 1
8 35 X^5 + X + 1 X^5 + X^2 X^2 + X + 1
9 39 X^5 + X^2 + X + 1 X^5 + X^3 X^2 + 1
10 45 X^5 + X^3 + X^2 + 1 X^5 + X^3 + X^2 + X X + 1
PROG
(PARI) is(n) = fromdigits(lift(Vec(gcd(Mod(1, 2) * Pol(binary(n)), Mod(1, 2) * Pol(binary(n+1))))), 2) != 1
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jan 19 2024
STATUS
approved
