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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.
1
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, 32, 12, 23, 45, 63, 72, 68, 59, 41, 15, 27, 56, 77, 90, 94, 87, 73, 47, 17, 30, 65, 92, 110, 119, 117, 106, 84, 54, 20, 34, 74, 107, 132, 146, 150, 142, 125, 98
OFFSET
1,2
COMMENTS
Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers.
LINKS
FORMULA
T(n,m) = Sum_{k=1...[n + m*n/r]} [1 - r + n*(r + m)/k], where r=log(2) and [ ]=floor.
EXAMPLE
Northwest corner:
1 3 5 9 11 16 18
2 7 14 21 29 38 45
4 13 24 36 50 63 77
6 19 35 53 72 90 110
8 26 46 68 94 119 146
10 32 59 87 117 150 181
12 41 73 106 142 180 219
The numbers k*(r+h), approximately:
(for k=1): 0.693 1.693 2.693 ...
(for k=2): 1.386 3.386 5.386 ...
(for k=3): 2.079 5.079 8.079 ...
Replacing each by its rank gives
1 3 5
2 7 14
4 13 24
MATHEMATICA
r = Log[2]; 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] (* A292962 array *)
Table[t[n - k + 1, k - 1], {n, 1, z}, {k, n, 1, -1}] // Flatten (* A292962 sequence *)
CROSSREFS
Cf. A182801.
Sequence in context: A203602 A249559 A182846 * A375306 A375112 A069196
KEYWORD
nonn,easy,tabl
AUTHOR
Clark Kimberling, Oct 05 2017
STATUS
approved