A078420 Numbers n such that h(n) = 3 h(n-1) where h(n) is the length of the sequence {n, f(n), f(f(n)), ...., 1} in the Collatz (or 3x + 1) problem. (The earliest "1" is meant.)

105, 548, 683, 1508, 3652, 4278, 4295, 8145, 8150, 9417, 9419, 18247, 18287, 18370, 18433, 18586, 18695, 18706, 18742, 18945, 22024, 22140, 22311, 22324, 22708, 22714, 25336, 25681, 25771, 25777, 25785, 25814, 44545, 44593, 46505, 46847

Offset

1,1

Comments

Recall that f(n) = n/2 if n is even; = 3n + 1 if n is odd.

Links

Table of n, a(n) for n=1..36.

Example

n, f(n), f(f(n)), ...., 1 for n = 105, 104, respectively, are: 105, 316, 158, 79, 238, 119, 358, 179, 538, 269, 808, 404, 202, 101, 304, 152, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1; 104, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, of lengths 39 = 3 x 13 and 13, respectively. Hence 105 belongs to the sequence.

Mathematica

f[n_] := If[EvenQ[n], n/2, 3n+1]; h[n_] := Module[{a, i}, i=n; a=1; While[i>1, a++; i=f[i]]; a]; Select[Range[2, 47000], 3h[ #-1]==h[ # ]&]
Flatten[Position[Partition[Table[Length[NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&]], {n, 50000}], 2, 1], _?(3#[[1]]==#[[2]]&), 1, Heads-> False]]+1 (* Harvey P. Dale, Apr 07 2018 *)

Crossrefs

Cf. A078418, A078419.

Sequence in context: A165069 A200834 A143041 * A152826 A133767 A166816

Adjacent sequences: A078417 A078418 A078419 * A078421 A078422 A078423

Keyword

nonn

Author

Joseph L. Pe, Dec 29 2002

Extensions

Extended by Robert G. Wilson v, Dec 30 2002

Status

approved