A308208 Least number k such that the determinant of the symmetric Hankel matrix formed by its decimal digits is equal to n negated.
0, 1101, 110, 12, 112, 23, 102, 34, 13, 45, 334, 56, 24, 67, 554, 14, 35, 89, 130, 667, 46, 25, 342, 887, 15, 889, 314, 36, 68, 241, 11022, 1164, 26, 47, 546, 16, 124, 425, 46730, 58, 37, 657, 13132, 415, 214, 27, 12850, 251, 17, 1707, 146, 235, 553, 2073, 114, 38, 59, 897, 526, 647
Offset: 0
Examples
| 1 1 0 |
a(2) = 110 because det | 1 0 1 | = -2
| 0 1 1 |
;
a(5) = 23 because det | 2 3 |
| 3 2 | = -5; etc.
Links
- Robert G. Wilson v, Table of n, a(n) for n = 0..10000
- Wikipedia, Hankel matrix
Crossrefs
Cf. A308110.
Programs
-
Maple
with(numtheory): with(linalg): P:=proc(q) local c, d, i, k, n, t: print(0); for i from 1 to q do for n from 1 to q do c:=convert(n, base, 10): t:=[]: for k from 1 to nops(c) do t:=[op(t), 0]: od: d:=t: t:=[]: for k from 1 to nops(c) do t:=[op(t), d]: t[k, -k]:=1: od: if det(evalm(toeplitz(c) &* t))=-i then print(n); break: fi: od: od: end: P(10^8);
-
Mathematica
f[n_] := Block[{k = 0}, While[id = IntegerDigits@ k; -Det[HankelMatrix[id, Reverse@ id]] != n, k++]; k]; Array[f, 60, 0]
Comments