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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
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
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
KEYWORD
nonn,easy,tabl
AUTHOR
Clark Kimberling, Oct 06 2017
STATUS
approved