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A306593 Least number k such that the determinant of the circulant matrix formed by its decimal digits is equal to n. 5
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 334, 65, 42, 76, 455, 41, 40, 98, 123, 667, 64, 52, 778, 788, 51, 50, 899, 63, 86, 7787, 2025885, 8788, 62, 74, 46996, 61, 60, 66898, 67997, 85, 73, 78998, 88899, 88999, 335, 72, 4579975, 878888, 71, 70, 10243, 5354, 355, 989999, 114 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Here only the least numbers are listed: e.g., a(75) = 1031, even if 10002110 also produces 75.

The sequence is infinite because any number of the form (91*10^n - 10) / 90 for n > 0 (A267623 or A283508) has the determinant of the circulant matrix equal to n but, in general, it is not the least possible term. - Giovanni Resta, Mar 06 2019

LINKS

Paolo P. Lava, Table of n, a(n) for n = 0..100

FORMULA

A177894(a(n)) = n when a(n) >= 0. - Rémy Sigrist, Feb 27 2019

EXAMPLE

                        | 3 3 4 |

a(10) = 334 because det | 4 3 3 | = 10

                        | 3 4 3 |

.

and 334 is the least number to have this property.

.

                          | 4 6 9 9 6 |

                          | 6 4 6 9 9 |

a(34) = 46996 because det | 9 6 4 6 9 | = 34

                          | 9 9 6 4 6 |

                          | 6 9 9 6 4 |

.

and 46996 is the least number to have this property.

MAPLE

with(linalg): P:=proc(q) local a, b, c, d, j, k, i, n, t;

print(0); 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=det(t) then print(n); break; fi; od; od; end: P(10^7);

PROG

(PARI) md(n) = my(d = if (n, digits(n), [0])); matdet(matrix(#d, #d, i, j, d[1+lift(Mod(j-i, #d))]));

a(n) = my(k=0); while(md(k) != n, k++); k; \\ Michel Marcus, Mar 20 2019

CROSSREFS

Cf. A177894, A219324, A267623, A283508, A306662, A323485, A323486.

Sequence in context: A004882 A306853 A308110 * A046469 A335151 A307887

Adjacent sequences:  A306590 A306591 A306592 * A306594 A306595 A306596

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, Feb 27 2019

STATUS

approved

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Last modified July 25 18:32 EDT 2021. Contains 346291 sequences. (Running on oeis4.)