OFFSET
0,2
COMMENTS
Assuming that the Collatz conjecture (also known as the 3x+1 conjecture) is true, this is a permutation of the positive integers; viz., every positive integer occurs exactly once. Conjecture: every row contains a pair of consecutive integers.
LINKS
FORMULA
Transpose of the array in A354236.
EXAMPLE
Corner:
1 2 4 8 16 32 64 128 256 512 1024
5 10 20 21 40 42 80 84 85 160 168
3 6 12 13 24 26 48 52 53 96 104
17 34 35 68 69 70 75 136 138 140 141
11 22 23 44 45 46 88 90 92 93 176
7 14 15 28 29 30 56 58 60 61 112
9 18 19 36 37 38 72 74 76 77 81
6 is in row 2 because the trajectory, (6, 3, 10, 5, 16, 4, 2, 1), has exactly 2 rises: 3 to 10, and 5 to 16.
MATHEMATICA
t = Table[Count[Differences[NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]], _? Positive], {n, 2048}]; (* after Harvey P. Dale, A006667 *)
r[n_] := Flatten[Position[t, n - 1]];
Column[Table[r[n], {n, 1, 21}]] (* array *)
u = Table[r[k][[n + 1 - k]], {n, 1, 12}, {k, 1, n}]
Flatten[u] (* sequence *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Sep 11 2024
STATUS
approved