Record pairs (n,k) of odd numbers n that have a record 3x+1 (Collatz) length k.
1, 1, 3, 6, 7, 12, 9, 14, 19, 15, 25, 17, 27, 71, 55, 72, 73, 74, 97, 76, 129, 78, 171, 80, 231, 82, 313, 84, 327, 92, 649, 93, 703, 109, 871, 114, 1161, 116, 2223, 117, 2463, 133, 2919, 138, 3711, 151, 6171, 166, 10971, 170, 13255, 175, 17647, 177, 23529, 179
1
Here we restrict n to be odd; sequence A006877 is similar, but without the restriction.
T. D. Noe, Plot of 64 pairs
T. D. Noe, Table of 64 pairs
Eric W. Weinstein, MathWorld: Collatz Problem
(Mma) nn = 11; Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, (3*# + 1)/2] &, n, # > 1 &]; c = Table[Length[Collatz[n]], {n, 1, 2^(nn - 1), 2}]; t = {{1, 1}}; Do[If[c[[i]] > t[[-1, 2]], AppendTo[t, {2 i - 1, c[[i]]}]], {i, Length[c]}]; Flatten[t]
Cf. A006877, S000560, S000561.
nonn
T. D. Noe, Apr 06 2015