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

1, 50, 648, 364, 20, 54, 21, 5000, 243, 10, 1636448, 324, 63414, 756, 73170, 432, 20043, 39366, 2121426, 46500, 6549795, 16236, 8490312, 303264, 200, 60450, 426465, 112, 27347, 2510460, 4464, 23616, 24354, 9282, 4253865, 3012552, 94017, 14022, 21411, 41000

Offset: 1

Author

Paolo P. Lava, Jan 17 2019

Keywords

• nonn
• base

Comments

a(10^j) = 10^j, with j >= 0.

Examples

			      det | 1 | = 1 = 1/1.
.
      det | 5 0 | = 25 = 50/2.
          | 0 5 |
.
          | 6 4 8 |
      det | 8 6 4 | = 216 = 648/3.
          | 4 8 6 |
		

Links

• Eric Weisstein's World of Mathematics, Circulant Matrix.
• Wikipedia, Circulant matrix.

Crossrefs

Cf. A219324, A323486.

Programs

Maple

with(linalg): P:=proc(q) local a,b,c,d,i,j,k,n,t;
for i from 1 to q do for n from 1 to q do
d:=ilog10(n)+1; a:=convert(n,base,10); c:=[];
for k from 1 to nops(a) do c:=[op(c),a[-k]]; od; t:=[op([]),c];
for k from 2 to d do b:=[op([]),c[nops(c)]]; for j from 1 to nops(c)-1 do
b:=[op(b),c[j]]; od;  c:=b; t:=[op(t),c]; od; if n=i*det(t) then
print(n); break; fi; od; od; end: P(10^7);