cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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.

Original entry on oeis.org

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

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Author

Clark Kimberling, Oct 05 2017

Keywords

Comments

Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers.

Examples

			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
		

Crossrefs

Programs

  • 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 *)

Formula

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