OFFSET
1,7
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.
FORMULA
For large n, a(n) ~ n * log(2)/log(6).
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Apr 30 2010
STATUS
approved