A292963 -id:A292963 - cp's OEIS frontend

A292964 Rectangular array by antidiagonals: T(n,m) = rank of n(1/e + m) when all the numbers k(1/e+h), for k>=1, h>=0, are jointly ranked.

1, 4, 2, 8, 10, 3, 13, 19, 16, 5, 17, 29, 32, 23, 6, 22, 40, 48, 44, 30, 7, 27, 52, 65, 68, 58, 37, 9, 34, 63, 82, 93, 89, 72, 46, 11, 38, 76, 102, 118, 120, 108, 87, 53, 12, 43, 88, 123, 144, 153, 149, 132, 101, 60, 14, 50, 99, 141, 171, 187, 189, 178, 155

Offset: 1

Clark Kimberling, Oct 05 2017

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

			Northwest corner:
1      4     8      13     17     22
2     10     19     29     40     52
3     16     32     48     65     82
5     23     44     68     93     118
6     30     58     89     120    153
7     37     72     108    149    189
9     46     87     132    178    228
The numbers k*(1/e+h), approximately:
(for k=1):   0.367   1.367  2.3667 ...
(for k=2):   0.735   2.735  4.735 ...
(for k=3):   1.103   4.103  7.103 ...
Replacing each by its rank gives
1    4     8
2    10    19
3    16    32

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

Cf. A182801, A292963.

r = 1/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]  (* A292964 array *)
Table[t[n - k + 1, k - 1], {n, 1, z}, {k, n, 1, -1}] // Flatten  (* A292964 sequence *)

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

cp's OEIS Frontend

A292964 Rectangular array by antidiagonals: T(n,m) = rank of n(1/e + m) when all the numbers k(1/e+h), for k>=1, h>=0, are jointly ranked.

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cp's OEIS Frontend

A292964 Rectangular array by antidiagonals: T(n,m) = rank of n*(1/e + m) when all the numbers k*(1/e+h), for k>=1, h>=0, are jointly ranked.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A292964 Rectangular array by antidiagonals: T(n,m) = rank of n(1/e + m) when all the numbers k(1/e+h), for k>=1, h>=0, are jointly ranked.