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A350160 Odd numbers whose Collatz trajectory does not include 5 as a term.

%I A350160 #14 Dec 19 2021 11:18:09
%S A350160 1,21,75,85,113,151,201,227,267,301,341,401,403,423,453,475,535,537,
%T A350160 605,633,635,713,715,803,805,847,891,909,951,953,955,1003,1069,1073,
%U A350160 1075,1129,1131,1191,1205,1267,1271,1273,1337,1365,1425,1427,1431,1433,1505
%N A350160 Odd numbers whose Collatz trajectory does not include 5 as a term.
%C A350160 Odd terms of A308149.
%C A350160 After a(2), each term's Collatz trajectory includes 256.
%C A350160 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 A350160 Jon E. Schoenfield, <a href="/A350160/b350160.txt">Table of n, a(n) for n = 1..10000</a>
%H A350160 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e A350160 The Collatz trajectories of the first few terms are as follows:
%e A350160 .
%e A350160    n  a(n)  trajectory
%e A350160   --  ----  ------------------------------------------------------------
%e A350160    1     1  1
%e A350160    2    21  21, 64, 32, 16, 8, 4, 2, 1
%e A350160    3    75  75, 226, 113, 340, 170, 85, 256, 128, 64, 32, 16, 8, 4, 2, 1
%e A350160    4    85  85, 256, 128, 64, 32, 16, 8, 4, 2, 1
%e A350160    5   113  113, 340, 170, 85, 256, 128, 64, 32, 16, 8, 4, 2, 1
%t A350160 Select[Range[1, 1500, 2], !MemberQ[NestWhileList[If[OddQ[#1], 3*#1 + 1, #1/2] &, #, #1 > 1 &], 5] &] (* _Amiram Eldar_, Dec 18 2021 *)
%Y A350160 Cf. A308149.
%K A350160 nonn
%O A350160 1,2
%A A350160 _Jon E. Schoenfield_, Dec 17 2021