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

Author

Paolo P. Lava, May 03 2019

Keywords

• nonn
• base

Examples

			                        | 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 |
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Wikipedia, Toeplitz matrix

Crossrefs

Cf. A306593.

Programs

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);