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URL: https://oeis.org/A337942

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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

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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..78.

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

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.

EXAMPLE

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

PROG

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

CROSSREFS

Sequence in context: A227287 A289236 A280172 * A341458 A089913 A257522

Adjacent sequences: A337939 A337940 A337941 * A337943 A337944 A337945

KEYWORD

nonn,tabl

AUTHOR

Rémy Sigrist, Oct 01 2020

STATUS

approved