

A258824


Least number k such that A258822(k) = n.


2




OFFSET

0,2


COMMENTS

If a(n) exists, a(n) > 10^6 for n > 3.
Excluding k = 24, for n = 2, after 29 and 34 iterations, you arrive at 29 and 34, respectively. Excluding k = 24, it appears all of the trajectories of the possible k values have length 48 or 49.
For n = 3, after 216, 234, and 252 iterations, you arrive at 216, 234, and 252, respectively. It appears all of the trajectories of the possible k values have length 317.


LINKS

Table of n, a(n) for n=0..3.


EXAMPLE

For n = 24, the '3x+1' map is as follows: 24 > 12 > 6 > 3 > 10 > 5 > 16 > 8 > 4 > 2 > 1. After the 3rd iteration, we reach 3 and after the 5 iteration, we reach 5. Since 12 is the smallest number to have exactly two occurrences, a(2) = 24. Note that the length of this trajectory is 11. For all other trajectories with exactly two occurrences, the length is either 48 or 49.


PROG

(PARI) Tvect(n)=v=[n]; while(n!=1, if(n%2, k=3*n+1; v=concat(v, k); n=k); if(!(n%2), k=n/2; v=concat(v, k); n=k)); v
n=0; m=1; while(m<10^3, d=Tvect(m); c=0; for(i=1, #d, if(d[i]==i1, c++)); if(c==n, print1(m, ", "); m=0; n++); m++)


CROSSREFS

Cf. A258822, A006370, A070165.
Sequence in context: A000722 A098679 A123851 * A120122 A068943 A100815
Adjacent sequences: A258821 A258822 A258823 * A258825 A258826 A258827


KEYWORD

nonn,hard,more,bref


AUTHOR

Derek Orr, Jun 11 2015


STATUS

approved



