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A293056 Rectangular array by antidiagonals: T(n,m) = rank of n*log(2)+m when all the numbers k*log(2)+h, for k >= 1, h >= 0, are jointly ranked. 1
1, 3, 2, 6, 5, 4, 11, 9, 8, 7, 17, 15, 13, 12, 10, 25, 22, 20, 18, 16, 14, 34, 31, 28, 26, 23, 21, 19, 45, 41, 38, 35, 32, 29, 27, 24, 57, 53, 49, 46, 42, 39, 36, 33, 30, 70, 66, 62, 58, 54, 50, 47, 43, 40, 37, 85, 80, 76, 72, 67, 63, 59, 55, 51, 48, 44, 101 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers. As an array, this is the interspersion of 1/log(2); see A283962.

LINKS

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

FORMULA

T(n,m) = Sum_{k=1...n + [m/r]} m+1+[(n-k)r], where r = log(2) and [ ]=floor.

EXAMPLE

Northwest corner:

1      3      6      11     17     25     34

2      5      9      15     22     31     41

4      8      13     20     28     38     49

7      12     18     26     35     46     58

10     16     23     32     42     54     67

14     21     29     39     50     63     77

19     27     36     47     59     73     88

24     33     43     55     68     83     99

30     40     51     64     78     94     111

The numbers k*r+h, approximately:

(for k=1):   0.693   1.693   2.693 ...

(for k=2):   1.386   2.386   3.386 ...

(for k=3):   2.079   3.079   4.079 ...

Replacing each k*r+h by its rank gives

1    3    6

2    5    9

4    8    13

MATHEMATICA

r = Log[2]; z = 12;

t[n_, m_] := Sum[Floor[1 + m + (n - k) r], {k, 1, n + Floor[m/r]}];

u = Table[t[n, m], {n, 1, z}, {m, 0, z}]

Grid[u] (* A293056 array *)

Table[t[n - k + 1, k - 1], {n, 1, z}, {k, n, 1, -1}] // Flatten  (* A293056 sequence *)

CROSSREFS

Cf. A283962.

Sequence in context: A277881 A145522 A283939 * A131968 A191740 A132665

Adjacent sequences:  A293053 A293054 A293055 * A293057 A293058 A293059

KEYWORD

nonn,easy,tabl

AUTHOR

Clark Kimberling, Oct 06 2017

STATUS

approved

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Last modified August 3 01:55 EDT 2021. Contains 346429 sequences. (Running on oeis4.)