The record values of the length of the reduced 3x-1 iteration.
1, 2, 3, 5, 11, 12, 18, 43, 50, 62, 78, 111, 121, 126, 130, 132, 161, 199, 238, 273, 276, 279, 306, 321, 368, 409
1
See S000253 for the location of these maxima.
T. D. Noe, Plot of 26 terms
(Mma) t = {}; mx = 0; Do[cnt = 1; m = n; While[If[EvenQ[m], m = m/2, m = (3*m - 1)/2]; m > n, cnt++]; If[cnt > mx, mx = cnt; AppendTo[t, {n, mx}]], {n, 1000000}]; Transpose[t][[2]]
Cf. S000252 (reduced iteration), S000253.
nonn,more
T. D. Noe, Sep 09 2014