This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A375157 #37 Oct 18 2024 18:27:35
%S A375157 2,43,462,458,4980,1887,18200,13405,37007,10508,200957,19554,125883,
%T A375157 151020,420079,51500,852186,77301,1196863,494117,644747,152723,
%U A375157 4745046,516750,1171643,1378716,3862900,352253,8755257,448846,7422697,2422746,3053960,2745778
%N 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.
%C A375157 Known positions of records occur at n = {2, 3, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36, 40, 42, 48}.
%C A375157 Conjecture: For n that is not prime, a(n) > a(PrimePi(n)), where PrimePi() is the prime counting function.
%e A375157 a(2) = 2, with one answer being the trivial zeros, and the other:
%e A375157 1 1 1 1 1 1 3 3 3 11_2 11_2 11_2
%e A375157 1 1 1 . 1 1 1 = 3 3 3 = 11_2 11_2 11_2
%e A375157 1 1 1 1 1 1 3 3 3 11_2 11_2 11_2
%e A375157 a(3), one of the true cases is:
%e A375157 0 1 2 2 1 0 2 4 6 2_3 11_3 20_3
%e A375157 2 2 2 . 1 1 1 = 6 8 8 = 20_3 22_3 22_3
%e A375157 1 2 2 1 1 1 4 7 8 11_3 21_3 22_3
%e A375157 a(10):
%e A375157 4 9 4 9 2 1 49 92 41
%e A375157 4 3 2 . 1 8 1 = 41 38 21
%e A375157 5 5 1 1 3 7 51 53 17
%K A375157 nonn,base
%O A375157 2,1
%A A375157 _Robert P. P. McKone_, Aug 01 2024