A258822 -id:A258822 - cp's OEIS frontend

A258824 Least number k such that A258822(k) = n.

1, 2, 24, 63105

Offset: 0

Derek Orr, Jun 11 2015

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.

			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.

Cf. A258822, A006370, A070165.

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]==i-1, c++)); if(c==n, print1(m, ", "); m=0; n++); m++)

A258823 Numbers m such that k iterations of m under the '3x+1' map yield k for some k.

Original entry on oeis.org

2, 7, 8, 10, 18, 19, 24, 26, 41, 43, 44, 45, 46, 48, 52, 53, 64, 65, 66, 67, 72, 74, 76, 77, 97, 98, 99, 100, 101, 102, 112, 116, 117, 120, 122, 144, 148, 149, 153, 156, 157, 158, 160, 172, 173, 174, 175, 209, 210, 211, 246, 247, 248, 249, 250, 252, 253, 254, 255, 260, 261, 262, 264, 266, 268, 269, 272

Offset: 1

Derek Orr, Jun 11 2015

nonn

Numbers m such that A258822(m) > 0.

			For m = 6, the '3x+1' map is as follows: 6 -> 3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1. For any possible k, after the k-th iteration, the result does not equal k. Thus 6 is not a member of this sequence.
For m = 7, the '3x+1' map is as follows: 7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1. After 10 iterations, we arrive at 10. So, 7 is a member of this sequence.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A258822, A006370, A070165.

kQ[n_]:=Module[{tr=Rest[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n, #>1&]], len}, len = Length[ tr];Count[Thread[{tr,Range[len]}],?(#[[1]] == #[[2]]&)]>0]; Select[Range[300],kQ] (* _Harvey P. Dale, Jan 13 2017 *)

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=1;while(n<10^3,d=Tvect(n); c=0; for(i=1, #d, if(d[i]==i-1,print1(n, ", ");break));n++)

cp's OEIS Frontend

A258824 Least number k such that A258822(k) = n.

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