

A078420


Numbers n such that h(n) = 3 h(n1) 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.)


2



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
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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



