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/r]} [1 - r + n*(r + m)/k], where r=log(2) and [ ]=floor.
EXAMPLE
Northwest corner:
1 3 5 9 11 16 18
2 7 14 21 29 38 45
4 13 24 36 50 63 77
6 19 35 53 72 90 110
8 26 46 68 94 119 146
10 32 59 87 117 150 181
12 41 73 106 142 180 219
The numbers k*(r+h), approximately:
(for k=1): 0.693 1.693 2.693 ...
(for k=2): 1.386 3.386 5.386 ...
(for k=3): 2.079 5.079 8.079 ...
Replacing each by its rank gives
1 3 5
2 7 14
4 13 24
MATHEMATICA
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Oct 05 2017
STATUS
approved