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A308110 Least number k such that the determinant of the symmetric Hankel matrix formed by its decimal digits is equal to n. 2
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 302, 65, 42, 76, 10320, 41, 40, 98, 522, 413, 64, 52, 354, 645, 51, 50, 142, 63, 86, 1534, 13112, 1387, 62, 74, 514, 61, 60, 635, 978, 85, 73, 1431, 502, 2677, 152, 72, 746, 625, 71, 70, 378, 2415, 254, 475, 366, 83, 95, 263, 33442 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The first nontrivial values for which a(n) = n are at n = 288 and n = 26825.

When a(n) < n: 168, 182, 232, 234, 252, 272, 280, 300, 304, 320, 324, 325, etc. - Robert G. Wilson v, May 14 2019

Records: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 302, 10320, 13112, 33442, 53242, 55262, 58493, 74959, 1021310, 1124232, 1272626, 1400230, 2034050, 2514162, 3043724, 4986388, 5604351, 106071534, 108162262, 117200232, 128580276, 134314966, 163332550, 165244716, 166811088, 225231732, 229330425, etc. - Robert G. Wilson v, May 15 2019

LINKS

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

Wikipedia, Hankel matrix

EXAMPLE

                        | 3 0 2 |

a(10) = 302 because det | 0 2 0 | = 10.

                        | 2 0 3 |

.

                         | 1 0 3 2 0 |

                         | 0 3 2 0 2 |

a(14)= 10320 because det | 3 2 0 2 3 | = 14.

                         | 2 0 2 3 0 |

                         | 0 2 3 0 1 |

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] (* Robert G. Wilson v, May 14 2019 *)

CROSSREFS

Cf. A306593, A307887, A308126.

Sequence in context: A229761 A004882 A306853 * A306593 A046469 A335151

Adjacent sequences:  A308107 A308108 A308109 * A308111 A308112 A308113

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, May 13 2019

EXTENSIONS

Offset corrected by Robert G. Wilson v, May 14 2019

STATUS

approved

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Last modified June 1 17:40 EDT 2020. Contains 334762 sequences. (Running on oeis4.)