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

1, 21, 75, 85, 113, 151, 201, 227, 267, 301, 341, 401, 403, 423, 453, 475, 535, 537, 605, 633, 635, 713, 715, 803, 805, 847, 891, 909, 951, 953, 955, 1003, 1069, 1073, 1075, 1129, 1131, 1191, 1205, 1267, 1271, 1273, 1337, 1365, 1425, 1427, 1431, 1433, 1505

Offset: 1

Author

Jon E. Schoenfield, Dec 17 2021

Keywords

• nonn

Comments

Odd terms of A308149.

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

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?

Examples

			The Collatz trajectories of the first few terms are as follows:
.
   n  a(n)  trajectory
  --  ----  ------------------------------------------------------------
   1     1  1
   2    21  21, 64, 32, 16, 8, 4, 2, 1
   3    75  75, 226, 113, 340, 170, 85, 256, 128, 64, 32, 16, 8, 4, 2, 1
   4    85  85, 256, 128, 64, 32, 16, 8, 4, 2, 1
   5   113  113, 340, 170, 85, 256, 128, 64, 32, 16, 8, 4, 2, 1
		

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A308149.

Programs

Mathematica

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