A074472 Length of iteration sequence of Collatz-function (A006370) when initial value is 3^n (A000244) and final cycle is followed once.

1, 8, 20, 112, 23, 97, 34, 77, 76, 44, 136, 135, 134, 133, 145, 206, 130, 191, 141, 96, 95, 262, 429, 92, 259, 395, 332, 256, 255, 391, 390, 389, 463, 462, 461, 460, 459, 458, 457, 456, 455, 454, 502, 501, 451, 499, 498, 753, 496, 495, 494, 749, 492, 747, 490

Offset

0,2

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Example

n=2: initial value=3^2, list of iterates is {9,28,14,7,22,11,34,17,52,26,13,50,20,10,5,16,8,4,2,1} length=a(2)=20; Observe that consecutive powers of 3 as arguments frequently provide iteration-lengths of consecutive integers, for instance n=10,11,12,13 give L=136,135,134,133 or n=88-96 result in L=1278-1271.

Mathematica

f[x_] := (1-Mod[x, 2])*(x/2)+(Mod[x, 2])*(3*x+1); f[1]=1; Table[1+Length[FixedPointList[f, 3^w]], {w, 1, 100}]

Crossrefs

Cf. A000244, A006370, A008884, A075484-A075488.

Sequence in context: A129550 A215181 A014584 * A175429 A297639 A094253

Adjacent sequences: A074469 A074470 A074471 * A074473 A074474 A074475

Keyword

nonn

Author

Labos Elemer, Sep 19 2002

Status

approved