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A292965
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Rectangular array by antidiagonals: T(n,m) = rank of n*(Pi + m) when all the numbers k*(Pi+h), for k >= 1, h >= 0, are jointly ranked.
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1
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1, 2, 5, 3, 8, 10, 4, 12, 16, 17, 6, 15, 22, 26, 23, 7, 20, 30, 35, 36, 31, 9, 25, 38, 46, 50, 47, 39, 11, 29, 45, 58, 64, 65, 59, 48, 13, 34, 54, 70, 78, 84, 79, 71, 56, 14, 41, 63, 83, 95, 103, 104, 97, 86, 67, 18, 44, 73, 94, 113, 123, 127, 124, 115, 99
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OFFSET
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1,2
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COMMENTS
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Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers.
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LINKS
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FORMULA
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T(n,m) = Sum_{k=1...[n + m*n/Pi]} [1 - Pi + n*(Pi + m)/k], where [ ]=floor.
Northwest corner:
1 2 3 4 6 7
5 8 12 15 20 25
10 16 22 30 38 45
17 26 35 46 58 70
23 36 50 64 78 95
31 47 65 84 103 123
39 59 79 104 127 153
The numbers k*(Pi+h), approximately:
(for k=1): 3.141 4.141 5.141 ...
(for k=2): 6.283 8.283 10.283 ...
(for k=3): 9.424 12.424 15.424 ...
Replacing each by its rank gives
1 2 3
5 8 12
10 16 22
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MATHEMATICA
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r = Pi; z = 12;
t[n_, m_] := Sum[Floor[1 - r + n*(r + m)/k], {k, 1, Floor[n + m*n/r]}];
u = Table[t[n, m], {n, 1, z}, {m, 0, z}]; TableForm[u] (* A292965 array *)
Table[t[n - k + 1, k - 1], {n, 1, z}, {k, n, 1, -1}] // Flatten (* A292965 sequence *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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