A307179 Numbers k such that k = i*j = 6*i + j, where i and j are integers

-25, -8, -3, 0, 24, 27, 32, 49

Offset

1,1

Comments

The sequence can be found by solving the equality i*j = 6*i + j. Re-arranging for j gives j = 6 + 6/(i-1). As both i and j must be integers this implies i - 1 must divide 6, thus the only values for i are -5,-2,-1,0,2,3,4,7. Finding the corresponding j and multiplying gives the 8 sequences values.

In general if we replace 6 by n, then the number of solutions will be 2*A000005(n), the lowest value will be -(n - 1)^2, and the highest value will be (n + 1)^2.

For values k>=0 this sequence gives the possible point scores in Australian Rules Football which equal the corresponding number of goals (worth six points) times the number of behinds (worth one point).

The number of solutions, in this case 8, is given by A062011(6). Robert G. Wilson v, Apr 10 2019

Links

Table of n, a(n) for n=1..8.

Example

The 8 solutions are:
--------------
i   j    k
--------------
-5   5   -25
-2   4   -8
-1   3   -3
0   0    0
2   12   24
3   9    27
4   8    32
7   7    49

Crossrefs

Cf. A000005

Sequence in context: A248583 A080203 A040605 * A065910 A096521 A215539

Adjacent sequences: A307176 A307177 A307178 * A307180 A307181 A307182

Keyword

sign,fini,full

Author

Scott R. Shannon, Mar 27 2019

Status

approved