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A255975 Rectangular array T(i,j) read by downwards antidiagonals: an interspersion associated with the fractal sequence A022328. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,easy,tabl
AUTHOR
Clark Kimberling, Mar 19 2015
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)