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

Author

Reinhard Zumkeller, Apr 18 2008

Keywords

• nonn

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

Crossrefs

Essentially the same sequence as A112695.

Cf. A006370, A006460.

Programs

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

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 *)