A378846 - OEIS

%I #11 Dec 27 2024 01:45:59

%S 1,2,4,3,6,11,13,9,18,35,25,47,33,63,45,81,95,117,127,85,57,113,133,

%T 89,97,65,129,87,173,225,231,293,309,377,261,273,545,671,465,485,597,

%U 647,741,529,353,705,471,941,1029,1241,837,577,385,257,513,343,229,153

%N Smallest starting x which takes n halving steps to reach the minimum of a cycle in the 3x-1 iteration.

%C 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.

%C The number of halving steps is A377524(x) so that a(n) = x is the smallest x for which A377524(x) = n.

%C 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.

%C 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.

%C 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.

%H Kevin Ryde, <a href="/A378846/b378846.txt">Table of n, a(n) for n = 0..932</a>

%H Kevin Ryde, <a href="/A378845/a378845.c.txt">C Code</a> (set count type HALF)

%o (C) /* See links. */

%Y Cf. A001281 (step), A377524 (number of halving steps).

%Y Cf. A378845 (with all steps), A378847 (with tripling steps).

%K nonn

%O 0,2

%A _Kevin Ryde_, Dec 15 2024