A255975 Rectangular array T(i,j) read by downwards antidiagonals: an interspersion associated with the fractal sequence A022328.

1, 3, 2, 7, 5, 4, 12, 10, 8, 6, 19, 16, 14, 11, 9, 27, 24, 21, 18, 15, 13, 37, 33, 30, 26, 23, 20, 17, 49, 44, 40, 36, 32, 29, 25, 22, 62, 57, 52, 47, 43, 39, 35, 31, 28, 77, 71, 66, 60, 55, 51, 46, 42, 38, 34, 93, 87, 81, 75, 69, 64, 59, 54, 50, 45, 41, 111

Offset

1,2

Comments

T(i,j) is the position of 2^i in the increasing sequence of the numbers 2^i*3^j, for i >= 0 and j >= 0; or equivalently, in the signature sequence of log(3)/log(2). A255975 is not equal to A051037; e.g., row 1 of A255975 includes 49, unlike A051037.

Links

Clark Kimberling, Antidiagonals n = 1..60, flattened

Example

Northwest corner:
1   3   7   12  19  27  37
2   5   10  16  24  33  44
4   8   14  21  30  40  52
6   11  18  26  36  47  60
9   15  23  32  43  55  69
13  20  29  39  51  64  79
The fractal sequence A022328 starts with 0, 1, 0, 2, 1, 3, 0, 2, 4, 1, 3, 0, 5, 2, 4, 1, 6, 3, ..., with 0 in positions 1, 3, 7, 12, ... as in row 1 of T; with 1 in positions 2, 5, 10, ... as in row 2; etc.

Mathematica

z = 400; t = Sort[Flatten[Table[2^i 3^j, {i, 0, z}, {j, 0, z}]]];
u = Table[IntegerExponent[t[[n]], 2], {n, 1, z}];
v = Table[Flatten[Position[u, n]], {n, 0, 20}];
TableForm[Table[v[[n, k]], {n, 1, 8}, {k, 1, 7}]]  (* A255975 array *)
Flatten[Table[v[[k, n - k + 1]], {n, 1, 16}, {k, 1, n}]] (* A255975 sequence *)

Crossrefs

Cf. A022428.

Sequence in context: A118834 A255547 A087468 * A167267 A097286 A278503

Adjacent sequences: A255972 A255973 A255974 * A255976 A255977 A255978

Keyword

nonn,easy,tabl

Author

Clark Kimberling, Mar 19 2015

Status

approved