-85,1

This sequence is labeled conjectural because (I think) we currently have no way of knowing whether there is some large n that has a long Collatz iteration. Sequence A220139 computes the trajectory for some large numbers, all of which have moderately small length (see A220140). The table below shows numbers in the same row. Notice that each row has only a few numbers. Row 15 is the first with 4 numbers: 26, 37, 103, 124. Row 324 is the first with 5 numbers: 336, 357, 370, 414, 440. Row 16028 has 6 numbers. Row 34937 has 7 numbers. No row in the first 10^7 rows has more than 7 numbers. This sequence is fairly linear; in the first 10^7 terms, no adjacent terms differ by more than 547.

T. D. Noe, Rows n = -85..1000 of irregular triangle, flattened

Eric Weisstein's World of Mathematics, Collatz Problem

Wikipedia, Collatz conjecture

Example:

row -85: 27

row -76: 31

row -69: 41

row -59: 54

row -58: 47, 55

row -46: 62

row -45: 63

row -43: 73

row -32: 71

row -29: 82

row -28: 83

row -22: 97

row -12: 94

row -11: 9, 95

row -10: 7

row -6: 108

row -5: 3, 109

row -4: 11, 14, 110

row -3: 6, 15, 18

row -2: 19, 91

row -1: 5

row 0: 1, 2

row 1: 4, 25

row 2: 12

row 3: 10, 13

row 4: 8, 17, 39

nn = 100; Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; t2 = Table[{n - Length[Collatz[n]], n}, {n, 2*nn}]; t3 = Select[t2, #[[1]] <= nn &]; Transpose[Sort[t3]][[2]]

Cf. A070165 (Collatz trajectories).

Cf. A008908 (length of trajectories).

Cf. A082984, A228014.

Sequence in context: A160394 A316729 A095387 * A031408 A324248 A377478

Adjacent sequences: A228057 A228058 A228059 * A228061 A228062 A228063

nonn,tabf

T. D. Noe, Aug 21 2013

approved