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

1,2

Links

Table of n, a(n) for n=1..17.

Eric Weisstein's World of Mathematics, Circulant Matrix.

Wikipedia, Circulant matrix.

Example

      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|

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);

Crossrefs

Cf. A219324, A323485.

Sequence in context: A248487 A172810 A231030 * A153139 A243974 A251274

Adjacent sequences: A323483 A323484 A323485 * A323487 A323488 A323489

Keyword

nonn,base,more

Author

Paolo P. Lava, Jan 17 2019

Extensions

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

Status

approved