A267969 Conjectured list of positive numbers k such that the Collatz-like map T: if x > 1 and x odd, x -> 5*x+1 and, if x even, x -> x/2, when started at k, eventually reaches a cycle that does not contain 1 (cf. A232711).

5, 10, 13, 17, 20, 26, 27, 33, 34, 40, 43, 52, 54, 66, 68, 80, 83, 86, 104, 105, 108, 132, 136, 160, 166, 172, 181, 185, 208, 210, 211, 215, 216, 245, 263, 264, 269, 272, 275, 320, 329, 332, 344, 362, 370, 416, 420, 422, 430, 432, 435, 453, 457, 463, 490, 526

Offset: 1

Author

Michel Lagneau, Jan 19 2016

Keywords

• nonn

Comments

A companion to A232711 (which conjecturally lists the numbers whose trajectory reaches 1), and A267970 (which conjecturally lists the numbers whose trajectory diverges).

This is conjectural in that there is no proof that the list is complete as far as it goes. Some of the terms in A267970 could belong to A232711 or this sequence if the trajectory is extended far enough. - N. J. A. Sloane, Jan 23 2016

It appears that the trajectories of all terms in this sequence reach one of two length 10 loops, one containing 13 and the other 17. This has been checked for terms up to 10^4 assuming trajectories with more than 10000 odd terms are infinite and also up to 10^6 assuming trajectories with more than 1000 odd terms are infinite. - Gary Detlefs, Jan 25 2022

Links

• Dmitry Kamenetsky, Table of n, a(n) for n = 1..2051

Crossrefs

Cf. A232711, A267970.

Programs

Maple

f:= proc(m,b,n) if n mod 2 = 1 then return m*n+1 else return n/2 fi end proc
F:= proc(m,b,n,i) option remember; if i=1 then return f(m,b,n) else return f(m,b,F(m,b,n,i-1)) fi end proc
for x from 1 to 1000 do for y from 1 to 1000 do if F(5,1,x,y)= 86 or F(5,1,x,y)=26 then print(x): x=x+1; y:=y+1 fi od od
# use print(x,y) to give the number of iterations needed to reach the cycle point
# Gary Detlefs, Jan 25 2022

Extensions

Entry revised by N. J. A. Sloane, Jan 23 2016

a(16)-a(55) added by Gary Detlefs, Jan 25 2022