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A292962 Rectangular array by antidiagonals: T(n,m) = rank of n*(r-1+m) when all the numbers k*(r+h), where r = log(2), k>=1, h>=0, are jointly ranked.

%I A292962 #4 Oct 05 2017 21:29:24
%S A292962 1,3,2,5,7,4,9,14,13,6,11,21,24,19,8,16,29,36,35,26,10,18,38,50,53,46,
%T A292962 32,12,23,45,63,72,68,59,41,15,27,56,77,90,94,87,73,47,17,30,65,92,
%U A292962 110,119,117,106,84,54,20,34,74,107,132,146,150,142,125,98
%N A292962 Rectangular array by antidiagonals:  T(n,m) = rank of n*(r-1+m) when all the numbers k*(r+h), where r = log(2), k>=1, h>=0, are jointly ranked.
%C A292962 Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers.
%H A292962 Clark Kimberling, <a href="/A292962/b292962.txt">Antidiagonals n=1..60, flattened</a>
%F A292962 T(n,m) = Sum_{k=1...[n + m*n/r]} [1 - r + n*(r + m)/k], where r=log(2) and [ ]=floor.
%e A292962 Northwest corner:
%e A292962 1    3    5    9    11   16   18
%e A292962 2    7    14   21   29   38   45
%e A292962 4    13   24   36   50   63   77
%e A292962 6    19   35   53   72   90   110
%e A292962 8    26   46   68   94   119  146
%e A292962 10   32   59   87   117  150  181
%e A292962 12   41   73   106  142  180  219
%e A292962 The numbers k*(r+h), approximately:
%e A292962 (for k=1):   0.693   1.693   2.693 ...
%e A292962 (for k=2):   1.386   3.386   5.386 ...
%e A292962 (for k=3):   2.079   5.079   8.079 ...
%e A292962 Replacing each by its rank gives
%e A292962 1    3    5
%e A292962 2    7    14
%e A292962 4    13   24
%t A292962 r = Log[2]; z = 12;
%t A292962 t[n_, m_] := Sum[Floor[1 - r + n*(r + m)/k], {k, 1, Floor[n + m*n/r]}];
%t A292962 u = Table[t[n, m], {n, 1, z}, {m, 0, z}]; TableForm[u]  (* A292962 array *)
%t A292962 Table[t[n - k + 1, k - 1], {n, 1, z}, {k, n, 1, -1}] // Flatten  (* A292962 sequence *)
%Y A292962 Cf. A182801.
%K A292962 nonn,easy,tabl
%O A292962 1,2
%A A292962 _Clark Kimberling_, Oct 05 2017