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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.
0
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
2,1
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.
EXAMPLE
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
CROSSREFS
Sequence in context: A349927 A112097 A354304 * A220270 A240550 A142199
KEYWORD
nonn,base
AUTHOR
Robert P. P. McKone, Aug 01 2024
STATUS
approved