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

Author

Scott R. Shannon, Mar 27 2019

Keywords

• sign
• fini
• full

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

Examples

			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