cp's OEIS Frontend

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).

%I A267969 #35 Jun 28 2024 23:17:58
%S A267969 5,10,13,17,20,26,27,33,34,40,43,52,54,66,68,80,83,86,104,105,108,132,
%T A267969 136,160,166,172,181,185,208,210,211,215,216,245,263,264,269,272,275,
%U A267969 320,329,332,344,362,370,416,420,422,430,432,435,453,457,463,490,526
%N 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).
%C A267969 A companion to A232711 (which conjecturally lists the numbers whose trajectory reaches 1), and A267970 (which conjecturally lists the numbers whose trajectory diverges).
%C A267969 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
%C A267969 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
%H A267969 Dmitry Kamenetsky, <a href="/A267969/b267969.txt">Table of n, a(n) for n = 1..2051</a>
%p A267969 f:= proc(m,b,n) if n mod 2 = 1 then return m*n+1 else return n/2 fi end proc
%p A267969 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
%p A267969 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
%p A267969 # use print(x,y) to give the number of iterations needed to reach the cycle point
%p A267969 # _Gary Detlefs_, Jan 25 2022
%Y A267969 Cf. A232711, A267970.
%K A267969 nonn
%O A267969 1,1
%A A267969 _Michel Lagneau_, Jan 19 2016
%E A267969 Entry revised by _N. J. A. Sloane_, Jan 23 2016
%E A267969 a(16)-a(55) added by _Gary Detlefs_, Jan 25 2022