A292963 Rectangular array by antidiagonals: T(n,m) = rank of n*(e + m) when all the numbers k*(e+h), for k>=1, h>=0, are jointly ranked.

1, 2, 4, 3, 7, 9, 5, 11, 15, 14, 6, 16, 22, 24, 20, 8, 19, 29, 34, 32, 27, 10, 25, 38, 45, 48, 43, 35, 12, 30, 46, 57, 62, 61, 54, 42, 13, 36, 55, 70, 79, 81, 76, 67, 50, 17, 40, 64, 83, 95, 101, 100, 92, 78, 58, 18, 47, 73, 97, 113, 122, 125, 120, 108, 89

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/e]} [1 - e + n*(e + m)/k], where [ ]=floor.

Example

Northwest corner:
1    2    3     5   6    8
4    7    11   16   19   25
9    15   22   29   38   46
14   24   34   45   57   70
20   32   48   62   79   95
27   43   61   81   101  122
35   54   76   100  125  152
42   67   92   120  151  181
The numbers k*(r+h), approximately:
(for k=1):   2.718  3.718  4.718 ...
(for k=2):   5.436   7.436   9.436 ...
(for k=3):   8.154   11.854   14.154 ...
Replacing each by its rank gives
1    2    3
4    7    14
9    15   22

Mathematica

r = E; 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]  (* A292963 array *)
Table[t[n - k + 1, k - 1], {n, 1, z}, {k, n, 1, -1}] // Flatten  (* A292963 sequence *)

Crossrefs

Cf. A182801, A292964.

Sequence in context: A225010 A235494 A292960 * A262759 A246268 A246267

Adjacent sequences: A292960 A292961 A292962 * A292964 A292965 A292966

Keyword

nonn,easy,tabl

Author

Clark Kimberling, Oct 05 2017

Status

approved