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A308208 Least number k such that the determinant of the symmetric Hankel matrix formed by its decimal digits is equal to n negated. 1

%I #16 Jul 15 2019 22:48:14

%S 0,1101,110,12,112,23,102,34,13,45,334,56,24,67,554,14,35,89,130,667,

%T 46,25,342,887,15,889,314,36,68,241,11022,1164,26,47,546,16,124,425,

%U 46730,58,37,657,13132,415,214,27,12850,251,17,1707,146,235,553,2073,114,38,59,897,526,647

%N Least number k such that the determinant of the symmetric Hankel matrix formed by its decimal digits is equal to n negated.

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

%H Robert G. Wilson v, <a href="/A308208/b308208.txt">Table of n, a(n) for n = 0..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hankel_matrix">Hankel matrix</a>

%e | 1 1 0 |

%e a(2) = 110 because det | 1 0 1 | = -2

%e | 0 1 1 |

%e ;

%e a(5) = 23 because det | 2 3 |

%e | 3 2 | = -5; etc.

%p with(numtheory): with(linalg): P:=proc(q) local c, d, i, k, n, t: print(0);

%p for i from 1 to q do for n from 1 to q do c:=convert(n, base, 10): t:=[]:

%p for k from 1 to nops(c) do t:=[op(t), 0]: od: d:=t: t:=[]:

%p for k from 1 to nops(c) do t:=[op(t), d]: t[k, -k]:=1: od:

%p if det(evalm(toeplitz(c) &* t))=-i then print(n); break: fi:

%p od: od: end: P(10^8);

%t f[n_] := Block[{k = 0}, While[id = IntegerDigits@ k; -Det[HankelMatrix[id, Reverse@ id]] != n, k++]; k]; Array[f, 60, 0]

%Y Cf. A308110.

%K nonn,base

%O 0,2

%A _Paolo P. Lava_ and _Robert G. Wilson v_, May 15 2019

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)