A177001 The number of 3x+1 steps in the Collatz iteration of A033491(n), the least number requiring n iterations.

0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 11, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 24, 24, 25, 25, 25, 26, 26, 27, 27, 28

Offset: 1

Author

T. D. Noe, Apr 30 2010

Keywords

• nonn

Comments

It appears that a(n) is the maximum number of 3x+1 steps for all numbers requiring n Collatz iterations, which is row n of A127824.

Examples

			24 is the smallest number that requires 10 Collatz iterations. The iteration uses two 3x+1 steps to produce 24, 12, 6, 3, 10, 5, 16, 8, 4, 2, 1. Hence a(10)=2.
		

Programs

Mathematica

col[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; Table[k = 1; While[Length[(y = col[k])] - 1 != n, k++]; Count[y, ?OddQ] - 1, {n, 80}] (* _Jayanta Basu, Jul 27 2013 *)

Formula

For large n, a(n) ~ n * log(2)/log(6).