A323486 Least number k such that the determinant of the circulant matrix formed by its decimal digits is equal to n*k.

1, 10168, 119700, 196, 1973082, 63980523693, 167037139360, 1350720096, 1543479071, 17239680, 4000206089, 219566358180, 104171259465, 2380649994, 113323907385, 14059155927, 19925280

Offset: 1

Author

Paolo P. Lava, Jan 17 2019

Keywords

• nonn
• base
• more

Examples

			      det | 1 | = 1 = 1*1.
.
          | 1 0 1 6 8|
          | 8 1 0 1 6|
      det | 6 8 1 0 1| = 20336 = 2*10168.
          | 1 6 8 1 0|
          | 0 1 6 8 1|
		

Links

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

Crossrefs

Cf. A219324, A323485.

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 i*n=det(t) then
print(n); break; fi; od; od; end: P(10^7);

Extensions

a(6)-a(17) from Giovanni Resta, Jan 21 2019