The number of Collatz (3x+1) iterations required for the n-th number in S000717.
1, 2, 8, 3, 6, 9, 17, 4, 20, 7, 15, 10, 18, 5, 13, 21, 16, 11, 24, 112, 19, 107, 27, 14, 22, 35, 110, 30, 105, 12, 25, 113, 33, 108, 28, 103, 23, 116, 36, 111, 31, 93, 106, 119, 26, 88, 39, 101, 114, 70, 34, 96, 47, 109, 122, 29, 42, 91, 104, 117, 37, 86, 55, 99
1
Every positive number occurs once in this sequence.
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]]]; lengths
Cf. S000717.
nonn,hard
T. D. Noe, Oct 09 2015