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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..40.

Eric W. Weisstein, MathWorld: 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

Cf. A219324, A323486.

Sequence in context: A156965 A240385 A282766 * A052460 A224168 A223859

Adjacent sequences:  A323482 A323483 A323484 * A323486 A323487 A323488

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, Jan 17 2019

STATUS

approved

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Last modified February 25 02:54 EST 2020. Contains 332217 sequences. (Running on oeis4.)