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A341314
Array read by antidiagonals: T(n,k) = (n+k)/gcd(n,k), n>=0, k>=0.
2
0, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 2, 4, 1, 1, 5, 5, 5, 5, 1, 1, 6, 3, 2, 3, 6, 1, 1, 7, 7, 7, 7, 7, 7, 1, 1, 8, 4, 8, 2, 8, 4, 8, 1, 1, 9, 9, 3, 9, 9, 3, 9, 9, 1, 1, 10, 5, 10, 5, 2, 5, 10, 5, 10, 1, 1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 1, 1, 12, 6, 4, 3, 12, 2, 12, 3, 4, 6, 12, 1
OFFSET
0,5
COMMENTS
We define gcd(0,0) = 0.
This sequence arose when studying Reed Kelly's A214551.
EXAMPLE
The array begins:
0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, ...
1, 3, 2, 5, 3, 7, 4, 9, 5, 11, 6, 13, 7, ...
1, 4, 5, 2, 7, 8, 3, 10, 11, 4, 13, 14, 5, ...
1, 5, 3, 7, 2, 9, 5, 11, 3, 13, 7, 15, 4, ...
1, 6, 7, 8, 9, 2, 11, 12, 13, 14, 3, 16, 17, ...
1, 7, 4, 3, 5, 11, 2, 13, 7, 5, 8, 17, 3, ...
1, 8, 9, 10, 11, 12, 13, 2, 15, 16, 17, 18, 19, ...
1, 9, 5, 11, 3, 13, 7, 15, 2, 17, 9, 19, 5, ...
1, 10, 11, 4, 13, 14, 5, 16, 17, 2, 19, 20, 7, ...
1, 11, 6, 13, 7, 3, 8, 17, 9, 19, 2, 21, 11, ...
1, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 2, 23, ...
1, 13, 7, 5, 4, 17, 3, 19, 5, 7, 11, 23, 2, ...
...
The first few antidiagonals are:
[0]
[1, 1]
[1, 2, 1]
[1, 3, 3, 1]
[1, 4, 2, 4, 1]
[1, 5, 5, 5, 5, 1]
[1, 6, 3, 2, 3, 6, 1]
[1, 7, 7, 7, 7, 7, 7, 1]
[1, 8, 4, 8, 2, 8, 4, 8, 1]
...
MAPLE
fa:= (m, n) -> if m=0 and n=0 then 0 else (m+n)/igcd(m, n); fi;
for m from 0 to 12 do lprint([seq(fa(m-n, n), n=0..m)]); od:
for m from 0 to 12 do lprint([seq(fa(m, n), n=0..12)]); od:
CROSSREFS
A054531 is a similar sequence. See also A341315, A341316.
Cf. A214551.
Sequence in context: A225043 A125605 A110570 * A335174 A082905 A141524
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Feb 17 2021
STATUS
approved