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

Author

Clark Kimberling, Mar 19 2015

Keywords

• nonn
• easy
• tabl

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A022428.

Programs

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 *)