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
CROSSREFS
KEYWORD
AUTHOR
Clark Kimberling, Oct 06 2017
STATUS
approved