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%I #19 Jan 25 2024 14:30:58
%S 1,10168,119700,196,1973082,63980523693,167037139360,1350720096,
%T 1543479071,17239680,4000206089,219566358180,104171259465,2380649994,
%U 113323907385,14059155927,19925280
%N Least number k such that the determinant of the circulant matrix formed by its decimal digits is equal to n*k.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CirculantMatrix.html">Circulant Matrix</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Circulant_matrix">Circulant matrix</a>.
%e det | 1 | = 1 = 1*1.
%e .
%e | 1 0 1 6 8|
%e | 8 1 0 1 6|
%e det | 6 8 1 0 1| = 20336 = 2*10168.
%e | 1 6 8 1 0|
%e | 0 1 6 8 1|
%p with(linalg): P:=proc(q) local a,b,c,d,i,j,k,n,t;
%p for i from 1 to q do for n from 1 to q do
%p d:=ilog10(n)+1; a:=convert(n,base,10); c:=[];
%p for k from 1 to nops(a) do c:=[op(c),a[-k]]; od; t:=[op([]),c];
%p for k from 2 to d do b:=[op([]),c[nops(c)]]; for j from 1 to nops(c)-1 do
%p b:=[op(b),c[j]]; od; c:=b; t:=[op(t),c]; od; if i*n=det(t) then
%p print(n); break; fi; od; od; end: P(10^7);
%Y Cf. A219324, A323485.
%K nonn,base,more
%O 1,2
%A _Paolo P. Lava_, Jan 17 2019
%E a(6)-a(17) from _Giovanni Resta_, Jan 21 2019
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