A346965 - OEIS

%I #57 Oct 09 2021 01:10:28

%S 0,0,1,0,1,1,3,0,4,1,3,1,2,3,2,0,3,4,4,1,1,3,2,1,5,2,17,3,4,2,16,0,6,

%T 3,2,4,4,4,6,1,17,1,6,3,4,2,16,1,5,5,5,2,2,17,17,3,7,4,6,2,3,16,15,0,

%U 6,6,5,3,3,2,16,4,18,4,2,4,5,6,6,1,4,17,17

%N a(n) is the number of ascending subsequences in reducing n to 1 using the Collatz reduction, or -1 if n refutes the Collatz conjecture.

%C In this sequence, a subsequence is considered ascending for as long as a (3*n + 1) / 2 step is required.

%H Douglas Boffey, <a href="/A346965/b346965.txt">Table of n, a(n) for n = 1..20000</a>

%H Douglas Boffey, <a href="/A346965/a346965.c.txt">Code used for generating b-file</a>

%F a(2^n) = 0.

%F a((2^n*(2*x+1)-1) * 2^y) = a(3^n*(2*x+1)-1) + 1, where x, y >= 0.

%e a(9) = 4, viz.

%e   9->14;

%e   14->7->11->17->26;

%e   26->13->20;

%e   20->10->5->8.

%o (C) /* A007814 */

%o int num_clear_bits(unsigned n) {

%o   if (n == 0)

%o     return -1;

%o   return log2(n & -n);

%o }

%o int A346965(unsigned n) {

%o   int x;

%o   int result = 0;

%o   n >>= num_clear_bits(n);

%o   while (n > 1) {

%o     x = num_clear_bits(n + 1);

%o     n = ((n >> x) + 1) * pow(3, x) - 1;

%o     n >>= num_clear_bits(n);

%o     ++result;

%o   }

%o   return result;

%o }

%Y Cf. A070168, A078719, A221469.

%K nonn

%O 1,7

%A _Douglas Boffey_, Aug 09 2021