A375157 The number of pairs of 3x3 matrices with elements from 0 to n such that the matrix product results in each element being the concatenation of the corresponding terms in base n.

2, 43, 462, 458, 4980, 1887, 18200, 13405, 37007, 10508, 200957, 19554, 125883, 151020, 420079, 51500, 852186, 77301, 1196863, 494117, 644747, 152723, 4745046, 516750, 1171643, 1378716, 3862900, 352253, 8755257, 448846, 7422697, 2422746, 3053960, 2745778

Offset: 2

Author

Robert P. P. McKone, Aug 01 2024

Keywords

• nonn
• base

Comments

Known positions of records occur at n = {2, 3, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36, 40, 42, 48}.

Conjecture: For n that is not prime, a(n) > a(PrimePi(n)), where PrimePi() is the prime counting function.

Examples

			a(2) = 2, with one answer being the trivial zeros, and the other:
1 1 1   1 1 1   3 3 3   11_2 11_2 11_2
1 1 1 . 1 1 1 = 3 3 3 = 11_2 11_2 11_2
1 1 1   1 1 1   3 3 3   11_2 11_2 11_2
a(3), one of the true cases is:
0 1 2   2 1 0   2 4 6    2_3 11_3 20_3
2 2 2 . 1 1 1 = 6 8 8 = 20_3 22_3 22_3
1 2 2   1 1 1   4 7 8   11_3 21_3 22_3
a(10):
4 9 4   9 2 1   49 92 41
4 3 2 . 1 8 1 = 41 38 21
5 5 1   1 3 7   51 53 17