A261870 - OEIS

%I #16 Dec 31 2024 06:47:36

%S 0,1,4,2,15,5,13,3,16,11,6,6,19,14,9,4,35,17,17,12,25,7,20,7,33,15,15,

%T 15,10,10,23,5,36,36,18,18,31,18,13,13,26,26,8,8,26,21,21,8,34,34,21,

%U 16,16,16,29,16,29,11,11,11,24,24,24,6,37,37,24,19,19,19,19,19,32,32,19,19,14,14,14,14,27,27,27,27,27,9,40,9,27,27,22,22,22,22,22,9,35,35,35,22

%N a(n) = minimal number of steps to get from n to 1, where a step is x -> 3x-1 if x is odd, or x -> either x/2 or 3x-1 if x is even.

%C The 3x-1 variation of Collatz conjecture would imply that this sequence is well defined. In turn, if this sequence is well-defined, then A109732 represents a permutation of the odd positive integers.

%H Kevin Ryde, <a href="/A261870/b261870.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Max Alekseyev)

%H Kevin Ryde, <a href="/A261870/a261870_1.c.txt">C Code</a>

%o (PARI) { A261870(n) = my(S, k); S=[n]; k=0; while( S[1]!=1, k++; S=vecsort( concat(apply(x->3*x-1, S), apply(x->x\2, select(x->x%2==0, S) )), , 8);  ); k } /* _Max Alekseyev_, Sep 03 2015 */

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

%Y Cf. A127885, A006577, A109732.

%K nonn

%O 1,3

%A _Max Alekseyev_, Sep 03 2015