A139399 Number of steps to reach a cycle in Collatz problem.

0, 0, 5, 0, 3, 6, 14, 1, 17, 4, 12, 7, 7, 15, 15, 2, 10, 18, 18, 5, 5, 13, 13, 8, 21, 8, 109, 16, 16, 16, 104, 3, 24, 11, 11, 19, 19, 19, 32, 6, 107, 6, 27, 14, 14, 14, 102, 9, 22, 22, 22, 9, 9, 110, 110, 17, 30, 17, 30, 17, 17, 105, 105, 4, 25, 25, 25, 12, 12, 12, 100, 20, 113, 20

Offset

1,3

Comments

a(1)=a(2)=a(4)=0 as A006370(A006370(A006370(x)))=x for x=1,2,4 [corrected by Rémy Sigrist, Jun 28 2020];

a(n) = A006577(n) - 2 for n > 2 (if the conjecture holds).

For n>2: let L = a(n) mod 3, then A006460(n) = if L=0 then 4 else L. - Reinhard Zumkeller, Nov 17 2013

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Collatz Problem

Index entries for sequences related to 3x+1 (or Collatz) problem

Mathematica

f[n_] := If[EvenQ[n], n/2, 3 n + 1];
a[n_] := If[n<3, 0, Length[NestWhileList[f, n, {#1, #2, #3} != {4, 2, 1}&, 3]] - 3];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Aug 08 2022 *)

Prog

(Haskell)
a139399 = f 0 where
   f k x = if x `elem` [1, 2, 4] then k else f (k + 1) (a006370 x)
-- Reinhard Zumkeller, Nov 17 2013

Crossrefs

Essentially the same sequence as A112695.

Cf. A006370, A006460.

Sequence in context: A197573 A019947 A193182 * A318525 A021669 A011511

Adjacent sequences: A139396 A139397 A139398 * A139400 A139401 A139402

Keyword

nonn

Author

Reinhard Zumkeller, Apr 18 2008

Status

approved