A373066 Numbers k such that the Hankel matrix formed using the digits of k is singular.

0, 100, 111, 124, 139, 200, 222, 248, 300, 333, 400, 421, 444, 469, 500, 555, 600, 666, 700, 777, 800, 842, 888, 900, 931, 964, 999, 10000, 10001, 10002, 10003, 10004, 10005, 10006, 10007, 10008, 10009, 10101, 10112, 10125, 10204, 10226, 10309, 11000, 11110, 11111, 11112, 11113, 11114, 11115

Offset

1,2

Comments

All terms have an odd number of digits.

If k is a term and not divisible by 10, then A004086(k) is a term.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(5) = 139 is a term because the Hankel matrix
[ 1 3 ]
[ 3 9 ]
formed from the digits 1,3,9 has determinant 0.

Maple

N:= 100: # for a(1) to a(N)
with(LinearAlgebra):
R:= 0: count:= 1:
for d from 1 by 2 while count < N do
  for x from 10^(d-1) to 10^d-1 while count < N do
    L:= convert(x, base, 10);
    if Determinant(HankelMatrix(L)) = 0 then
       R:= R, x;
       count:= count+1;
    fi
od od:
R;

Crossrefs

Cf. A004086.

Sequence in context: A281193 A285776 A226032 * A286699 A171222 A286739

Adjacent sequences: A373063 A373064 A373065 * A373067 A373068 A373069

Keyword

nonn,base

Author

Robert Israel, May 21 2024

Status

approved