A357372 Square array A(n, k), n, k > 0, read by antidiagonals; A(n, k) is the numerator of 1/n + 1/k.
2, 3, 3, 4, 1, 4, 5, 5, 5, 5, 6, 3, 2, 3, 6, 7, 7, 7, 7, 7, 7, 8, 2, 8, 1, 8, 2, 8, 9, 9, 1, 9, 9, 1, 9, 9, 10, 5, 10, 5, 2, 5, 10, 5, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 3, 4, 3, 12, 1, 12, 3, 4, 3, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13
Offset: 1
Examples
Array A(n, k) begins:
n\k | 1 2 3 4 5 6 7 8 9 10 11 12 13
----+---------------------------------------------------
1 | 2 3 4 5 6 7 8 9 10 11 12 13 14
2 | 3 1 5 3 7 2 9 5 11 3 13 7 15
3 | 4 5 2 7 8 1 10 11 4 13 14 5 16
4 | 5 3 7 1 9 5 11 3 13 7 15 1 17
5 | 6 7 8 9 2 11 12 13 14 3 16 17 18
6 | 7 2 1 5 11 1 13 7 5 4 17 1 19
7 | 8 9 10 11 12 13 2 15 16 17 18 19 20
8 | 9 5 11 3 13 7 15 1 17 9 19 5 21
9 | 10 11 4 13 14 5 16 17 2 19 20 7 22
10 | 11 3 13 7 3 4 17 9 19 1 21 11 23
11 | 12 13 14 15 16 17 18 19 20 21 2 23 24
12 | 13 7 5 1 17 1 19 5 7 11 23 1 25
13 | 14 15 16 17 18 19 20 21 22 23 24 25 2
Links
- Rémy Sigrist, Table of n, a(n) for n = 1..10011
Programs
-
Mathematica
Flatten[Table[Numerator[1/i + 1/(m - i)], {m, 13}, {i, m - 1}]] -
PARI
A(n,k) = numerator(1/n + 1/k)
Formula
A(n, k) = (n + k) / gcd(n + k, n*k).
A(n, k) = A(k, n).
A(n, 1) = n + 1.
A(n, n) = A000034(n).
A(n, n+1) = 2*n + 1.
Comments