A307887 Least number k such that the determinant of the symmetric Toeplitz matrix formed by its decimal digits is equal to n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 433, 65, 42, 76, 455, 41, 40, 98, 457, 766, 64, 52, 243, 788, 51, 50, 413, 63, 86, 142, 21024, 3055, 62, 74, 645, 61, 60, 524, 25624, 85, 73, 756, 20031, 514, 412, 72, 23688, 152, 71, 70, 641, 364, 355, 2542, 245, 83, 95, 798, 625

Offset

0,3

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Wikipedia, Toeplitz matrix

Example

                        | 4 3 3 |
a(10) = 433 because det | 3 4 3 | = 10.
                        | 3 3 4 |
.
                         | 2 5 6 2 4 |
                         | 5 2 5 6 2 |
a(38)= 25624 because det | 6 5 2 5 6 | = 38.
                         | 2 6 5 2 5 |
                         | 4 2 6 5 2 |

Maple

with(numtheory): with(linalg): P:=proc(q) local a, c, i, k, n; print(0);
for i from 1 to q do for n from 1 to q do a:=convert(n, base, 10):
c:=[]: for k from 1 to nops(a) do c:=[op(c), a[-k]]: od:
if det(toeplitz(c))=i then print(n); break: fi: od: od: end: P(10^6);

Crossrefs

Cf. A306593.

Sequence in context: A046469 A335151 A065110 * A362843 A344822 A004893

Adjacent sequences: A307884 A307885 A307886 * A307888 A307889 A307890

Keyword

nonn,base

Author

Paolo P. Lava, May 03 2019

Status

approved