cp's OEIS Frontend

A378846 Smallest starting x which takes n halving steps to reach the minimum of a cycle in the 3x-1 iteration.

%I A378846 #11 Dec 27 2024 01:45:59
%S A378846 1,2,4,3,6,11,13,9,18,35,25,47,33,63,45,81,95,117,127,85,57,113,133,
%T A378846 89,97,65,129,87,173,225,231,293,309,377,261,273,545,671,465,485,597,
%U A378846 647,741,529,353,705,471,941,1029,1241,837,577,385,257,513,343,229,153
%N A378846 Smallest starting x which takes n halving steps to reach the minimum of a cycle in the 3x-1 iteration.
%C A378846 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 A378846 The number of halving steps is A377524(x) so that a(n) = x is the smallest x for which A377524(x) = n.
%C A378846 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 A378846 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 A378846 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 A378846 Kevin Ryde, <a href="/A378846/b378846.txt">Table of n, a(n) for n = 0..932</a>
%H A378846 Kevin Ryde, <a href="/A378845/a378845.c.txt">C Code</a> (set count type HALF)
%o A378846 (C) /* See links. */
%Y A378846 Cf. A001281 (step), A377524 (number of halving steps).
%Y A378846 Cf. A378845 (with all steps), A378847 (with tripling steps).
%K A378846 nonn
%O A378846 0,2
%A A378846 _Kevin Ryde_, Dec 15 2024