Numbers whose Collatz (3x+1) iteration requires a different number of steps than any smaller number.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 17, 18, 22, 24, 25, 27, 28, 31, 33, 34, 36, 39, 41, 43, 47, 48, 49, 54, 57, 62, 65, 71, 72, 73, 78, 82, 86, 91, 94, 97, 98, 103, 105, 107, 108, 111, 114, 121, 123, 124, 129, 130, 135, 137, 142, 145, 153, 155, 159
1
The sequence S000718 gives the number of iterations required by these numbers.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Eric W. Weisstein, Collatz Problem
(Mma) Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; lengths = {}; t = {}; n = 0; While[Length[t] < 100, n++; k = Length[Collatz[n]]; If[! MemberQ[lengths, k], AppendTo[lengths, k]; AppendTo[t, n]]]; t
nonn,hard
T. D. Noe, Oct 09 2015