A337942 Table read by antidiagonals: T(n, k) is the least positive m such that (m*n) mod k = (m*k) mod n, with n > 0 and k > 0.

1, 2, 2, 3, 1, 3, 4, 5, 5, 4, 5, 2, 1, 2, 5, 6, 3, 2, 2, 3, 6, 7, 3, 2, 1, 2, 3, 7, 8, 11, 2, 7, 7, 2, 11, 8, 9, 4, 17, 5, 1, 5, 17, 4, 9, 10, 5, 11, 13, 3, 3, 13, 11, 5, 10, 11, 5, 3, 2, 3, 1, 3, 2, 3, 5, 11, 12, 17, 7, 3, 28, 10, 10, 28, 3, 7, 17, 12

Offset: 1

Author

Rémy Sigrist, Oct 01 2020

Keywords

• nonn
• tabl

Examples

			Array T(n, k) begins:
  n\k|  1   2   3   4   5   6   7   8   9  10
  ---+---------------------------------------
    1|  1   2   3   4   5   6   7   8   9  10
    2|  2   1   5   2   3   3  11   4   5   5
    3|  3   5   1   2   2   2  17  11   3   7
    4|  4   2   2   1   7   5  13   2   3   3
    5|  5   3   2   7   1   3   3  28  13   2
    6|  6   3   2   5   3   1  10   2   5   2
    7|  7  11  17  13   3  10   1   4   4  25
    8|  8   4  11   2  28   2   4   1  13   7
    9|  9   5   3   3  13   5   4  13   1   5
   10| 10   5   7   3   2   2  25   7   5   1
		

Links

• Rémy Sigrist, Scatterplot of (x, y) such that T(x, y) is even and 1 <= x, y, <= 1000
• Rémy Sigrist, Scatterplot of (x, y) such that T(x, y) divides x*y and 1 <= x, y, <= 1000

Crossrefs

Cf. A123684.

Programs

PARI

T(n,k) = for (m=1, oo, if ((m*n)%k==(m*k)%n, return (m)))

Formula

T(n, k) = T(k, n) <= k*n.

T(n, n) = 1.

T(n, 1) = n.

T(n, n^2) = n.

T(n, n^3) = n^2.

T(n, n^k) = n^(k-1) for any k > 0.

T(n, n+1) = A123684(n+1) for any n > 2.