A220071 Difference between number of halving steps and number of tripling steps needed to reach 1 in '3x+1' problem.

0, 1, 3, 2, 3, 4, 6, 3, 7, 4, 6, 5, 5, 7, 7, 4, 6, 8, 8, 5, 5, 7, 7, 6, 9, 6, 29, 8, 8, 8, 28, 5, 10, 7, 7, 9, 9, 9, 12, 6, 29, 6, 11, 8, 8, 8, 28, 7, 10, 10, 10, 7, 7, 30, 30, 9, 12, 9, 12, 9, 9, 29, 29, 6, 11, 11, 11, 8, 8, 8, 28, 10, 31, 10, 8, 10, 10, 13

Offset: 1

Author

Jayanta Basu, Feb 19 2013

Keywords

• nonn

Comments

This sequence can also be defined as: a(1) = 0; thereafter a(2*k) = a(k) + 1, a(2*k+1) = a(6*k+4) - 1. - Gionata Neri, Jul 17 2016

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006577, A006666, A006667, A014682.

Programs

Maple

a:= proc(n) option remember; `if`(n<2, 0,
      `if`(irem(n, 2)=0, 1+a(n/2), a((3*n+1)/2)))
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Feb 19 2013

Mathematica

coll[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Table[(x = Count[coll[n], ?EvenQ]) - (Length[coll[n]] - x - 1), {n, 78}] (* _Jayanta Basu, Aug 15 2013 *)

Formula

a(n) = A006666(n) - A006667(n).

a(n) = a(A085062(n)) + 1 for n >= 2. - Alan Michael Gómez Calderón, Jan 26 2025

Extensions

More terms from Alois P. Heinz, Feb 19 2013