A078419 Numbers n such that h(n) = 2 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.)

2, 5, 22, 495, 559, 2972, 3092, 3124, 3147, 3153, 3184, 3367, 3711, 3748, 3857, 3921, 3982, 4450, 4767, 17019, 17708, 17769, 17771, 17782, 17796, 17825, 17835, 17857, 17863, 17892, 18079, 18082, 18139, 18298, 18422, 18580, 18644, 18688, 18784

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..39.

Example

n, f(n), f(f(n)), ...., 1 for n = 22, 21, respectively, are: 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1; 21, 64, 32, 16, 8, 4, 2, 1. Hence h(22) = 16 = 2 * 8 = h(21) and 22 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, 18800], 2h[ #-1]==h[ # ]&]

Crossrefs

Cf. A078418, A078420.

Sequence in context: A050994 A326959 A034384 * A241428 A342386 A070281

Adjacent sequences: A078416 A078417 A078418 * A078420 A078421 A078422

Keyword

nonn

Author

Joseph L. Pe, Dec 29 2002

Extensions

Extended by Robert G. Wilson v, Dec 30 2002

Status

approved