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

0,2

Comments

Records: 0, 1101, 11022, 46730, 52324, 54160, 1125004, 1162232, 1205240, 1252514, 1341680, 1663828, 3357554, 3741424, 4561735, 5069138, 9436293, 104562436, 122775666, 160205152, 165525440, 224394816, etc.

Links

Robert G. Wilson v, Table of n, a(n) for n = 0..10000

Wikipedia, Hankel matrix

Example

                       | 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.

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]

Crossrefs

Cf. A308110.

Sequence in context: A277864 A278592 A278443 * A290684 A290852 A283133

Adjacent sequences: A308205 A308206 A308207 * A308209 A308210 A308211

Keyword

nonn,base

Author

Paolo P. Lava and Robert G. Wilson v, May 15 2019

Status

approved