Where records occur in the 3x-1 iteration.
1, 2, 3, 6, 9, 17, 21, 33, 57, 65, 87, 153, 305, 321, 641, 677, 903, 1209, 1425, 1689, 2981, 3975, 6929, 7301, 9735, 11025, 18273, 21657, 38501, 47897, 54021, 54081, 64025, 64097, 85463, 113951, 126465, 149889, 266469, 304901, 361365, 482817, 858341
1
See S000242 for the record values.
T. D. Noe, Plot of 63 terms
T. D. Noe, Table of 63 terms
(Mma) t = {{1, 1}}; mx = 1; Do[s = {n}; m = n; While[If[EvenQ[m], m = m/2, m = (3*m - 1)/2]; ! MemberQ[s, m], AppendTo[s, m]]; If[Length[s] > mx, mx = Length[s]; AppendTo[t, {n, mx}]], {n, 2, 1000000}]; Transpose[t][[1]]
nonn
T. D. Noe, Sep 04 2014