A350160 - OEIS

A350160

Odd numbers whose Collatz trajectory does not include 5 as a term.

%I #14 Dec 19 2021 11:18:09

%S 1,21,75,85,113,151,201,227,267,301,341,401,403,423,453,475,535,537,

%T 605,633,635,713,715,803,805,847,891,909,951,953,955,1003,1069,1073,

%U 1075,1129,1131,1191,1205,1267,1271,1273,1337,1365,1425,1427,1431,1433,1505

%N Odd numbers whose Collatz trajectory does not include 5 as a term.

%C Odd terms of A308149.

%C After a(2), each term's Collatz trajectory includes 256.

%C A plot of a(n)/n vs. n has an interesting quasiperiodic form with a decreasing frequency. Does lim_{n->infinity} a(n)/n equal 32?

%H Jon E. Schoenfield, <a href="/A350160/b350160.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%e The Collatz trajectories of the first few terms are as follows:

%e .

%e n a(n) trajectory

%e -- ---- ------------------------------------------------------------

%e 1 1 1

%e 2 21 21, 64, 32, 16, 8, 4, 2, 1

%e 3 75 75, 226, 113, 340, 170, 85, 256, 128, 64, 32, 16, 8, 4, 2, 1

%e 4 85 85, 256, 128, 64, 32, 16, 8, 4, 2, 1

%e 5 113 113, 340, 170, 85, 256, 128, 64, 32, 16, 8, 4, 2, 1

%t Select[Range[1, 1500, 2], !MemberQ[NestWhileList[If[OddQ[#1], 3*#1 + 1, #1/2] &, #, #1 > 1 &], 5] &] (* _Amiram Eldar_, Dec 18 2021 *)

%Y Cf. A308149.

%K nonn

%O 1,2

%A _Jon E. Schoenfield_, Dec 17 2021