OFFSET
1,3
COMMENTS
This sequence has similarities with Stern's diatomic series (A002487) as it equals its even bisection and two consecutive terms are always coprime.
For any prime number p, p is the first multiple of p to appear in the sequence.
All prime numbers appear in the sequence, in natural order.
Will every positive integer appear?
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..8192
Rémy Sigrist, PARI program
FORMULA
gcd(a(n), a(n+1)) = 1.
EXAMPLE
a(1) = 1 by definition.
a(2) = a(1) = 1.
a(3) must be coprime to a(1) = 1 and a(2) = 1; we chose a(3) = 2.
a(4) = a(2) = 1.
a(5) must be coprime to a(2) = 1 and a(3) = 2; we chose a(5) = 3.
a(6) = a(3) = 2.
a(7) must be coprime to a(3) = 2 and a(4) = 1; we chose a(7) = 5.
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Dec 10 2023
STATUS
approved