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A323485 Least number k such that the determinant of the circulant matrix formed by its decimal digits is equal to k/n.

%I A323485 #21 Jan 25 2024 14:31:02
%S A323485 1,50,648,364,20,54,21,5000,243,10,1636448,324,63414,756,73170,432,
%T A323485 20043,39366,2121426,46500,6549795,16236,8490312,303264,200,60450,
%U A323485 426465,112,27347,2510460,4464,23616,24354,9282,4253865,3012552,94017,14022,21411,41000
%N A323485 Least number k such that the determinant of the circulant matrix formed by its decimal digits is equal to k/n.
%C A323485 a(10^j) = 10^j, with j >= 0.
%H A323485 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CirculantMatrix.html">Circulant Matrix</a>.
%H A323485 Wikipedia, <a href="https://en.wikipedia.org/wiki/Circulant_matrix">Circulant matrix</a>.
%e A323485       det | 1 | = 1 = 1/1.
%e A323485 .
%e A323485       det | 5 0 | = 25 = 50/2.
%e A323485           | 0 5 |
%e A323485 .
%e A323485           | 6 4 8 |
%e A323485       det | 8 6 4 | = 216 = 648/3.
%e A323485           | 4 8 6 |
%p A323485 with(linalg): P:=proc(q) local a,b,c,d,i,j,k,n,t;
%p A323485 for i from 1 to q do for n from 1 to q do
%p A323485 d:=ilog10(n)+1; a:=convert(n,base,10); c:=[];
%p A323485 for k from 1 to nops(a) do c:=[op(c),a[-k]]; od; t:=[op([]),c];
%p A323485 for k from 2 to d do b:=[op([]),c[nops(c)]]; for j from 1 to nops(c)-1 do
%p A323485 b:=[op(b),c[j]]; od;  c:=b; t:=[op(t),c]; od; if n=i*det(t) then
%p A323485 print(n); break; fi; od; od; end: P(10^7);
%Y A323485 Cf. A219324, A323486.
%K A323485 nonn,base
%O A323485 1,2
%A A323485 _Paolo P. Lava_, Jan 17 2019