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/Pi]} [1 - Pi + n*(Pi + m)/k], where [ ]=floor.
Northwest corner:
1 2 3 4 6 7
5 8 12 15 20 25
10 16 22 30 38 45
17 26 35 46 58 70
23 36 50 64 78 95
31 47 65 84 103 123
39 59 79 104 127 153
The numbers k*(Pi+h), approximately:
(for k=1): 3.141 4.141 5.141 ...
(for k=2): 6.283 8.283 10.283 ...
(for k=3): 9.424 12.424 15.424 ...
Replacing each by its rank gives
1 2 3
5 8 12
10 16 22
MATHEMATICA
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Oct 06 2017
STATUS
approved