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, 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

Clark Kimberling, Antidiagonals n=1..60, flattened

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 * A069196 A222209 A118320

Adjacent sequences: A292959 A292960 A292961 * A292963 A292964 A292965

Keyword

nonn,easy,tabl

Author

Clark Kimberling, Oct 05 2017

Status

approved