Record pairs (n,k) of numbers n that have a record 3x+1 (Collatz) length k, the number of terms > n.
3, 5, 7, 12, 9, 13, 27, 102, 703, 131, 937, 133, 1249, 134, 2223, 141, 2463, 159, 2919, 165, 10087, 170, 13449, 171, 35655, 222, 60975, 254, 142587, 273, 381727, 282, 626331, 310, 837799, 342, 1126015, 364, 1394431, 380, 6206655, 406, 6649279, 492
1
See the uncoupled pairs in S000943 and S000944.
T. D. Noe, Plot of 44 terms
Eric W. Weinstein, MathWorld: Collatz Problem
(Mma) Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; t = {}; mx = 0; Do[len = Length[Select[Collatz[n], # > n &]]; If[len > mx, mx = len; AppendTo[t, {n, mx}]];, {n, 100000}]; Flatten[t]
nonn
T. D. Noe, Aug 29 2016