OFFSET
0,2
COMMENTS
Each step is x -> 3x-1 if x odd, or x -> x/2 if x even (A001281) and here only the halving steps x/2 are counted.
The number of halving steps is A377524(x) so that a(n) = x is the smallest x for which A377524(x) = n.
a(n) <= 2*a(n-1) is an upper bound since x = 2*a(n-1) is a candidate for a(n) by first step x -> x/2.
All even terms are a(n) = 2*a(n-1), since any smaller even a(n) would imply a smaller a(n-1) by first step x -> x/2.
No term is of the form y = 6*k + 2, apart from a(1)=2, since odd x = 2*k+1 takes a tripling step to 3*x-1 = y and x is a smaller start with the same number of halvings as y.
LINKS
Kevin Ryde, Table of n, a(n) for n = 0..932
Kevin Ryde, C Code (set count type HALF)
PROG
(C) /* See links. */
CROSSREFS
KEYWORD
nonn
AUTHOR
Kevin Ryde, Dec 15 2024
STATUS
approved