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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.
4
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
1,2
COMMENTS
a(10^j) = 10^j, with j >= 0.
LINKS
Eric Weisstein's World of Mathematics, Circulant Matrix.
Wikipedia, Circulant matrix.
EXAMPLE
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 |
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);
CROSSREFS
Sequence in context: A156965 A240385 A282766 * A052460 A224168 A223859
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Jan 17 2019
STATUS
approved