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%I #12 Mar 27 2015 09:01:00
%S 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,
%T 20,17,49,44,40,36,32,29,25,22,62,57,52,47,43,39,35,31,28,77,71,66,60,
%U 55,51,46,42,38,34,93,87,81,75,69,64,59,54,50,45,41,111
%N Rectangular array T(i,j) read by downwards antidiagonals: an interspersion associated with the fractal sequence A022328.
%C 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.
%H Clark Kimberling, <a href="/A255975/b255975.txt">Antidiagonals n = 1..60, flattened </a>
%e Northwest corner:
%e 1 3 7 12 19 27 37
%e 2 5 10 16 24 33 44
%e 4 8 14 21 30 40 52
%e 6 11 18 26 36 47 60
%e 9 15 23 32 43 55 69
%e 13 20 29 39 51 64 79
%e 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.
%t z = 400; t = Sort[Flatten[Table[2^i 3^j, {i, 0, z}, {j, 0, z}]]];
%t u = Table[IntegerExponent[t[[n]], 2], {n, 1, z}];
%t v = Table[Flatten[Position[u, n]], {n, 0, 20}];
%t TableForm[Table[v[[n, k]], {n, 1, 8}, {k, 1, 7}]] (* A255975 array *)
%t Flatten[Table[v[[k, n - k + 1]], {n, 1, 16}, {k, 1, n}]] (* A255975 sequence *)
%Y Cf. A022428.
%K nonn,easy,tabl
%O 1,2
%A _Clark Kimberling_, Mar 19 2015
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