A373066 - OEIS

%I #6 May 27 2024 22:59:09

%S 0,100,111,124,139,200,222,248,300,333,400,421,444,469,500,555,600,

%T 666,700,777,800,842,888,900,931,964,999,10000,10001,10002,10003,

%U 10004,10005,10006,10007,10008,10009,10101,10112,10125,10204,10226,10309,11000,11110,11111,11112,11113,11114,11115

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

%C All terms have an odd number of digits.

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

%H Robert Israel, <a href="/A373066/b373066.txt">Table of n, a(n) for n = 1..10000</a>

%e a(5) = 139 is a term because the Hankel matrix

%e [ 1 3 ]

%e [ 3 9 ]

%e formed from the digits 1,3,9 has determinant 0.

%p N:= 100: # for a(1) to a(N)

%p with(LinearAlgebra):

%p R:= 0: count:= 1:

%p for d from 1 by 2 while count < N do

%p   for x from 10^(d-1) to 10^d-1 while count < N do

%p     L:= convert(x,base,10);

%p     if Determinant(HankelMatrix(L)) = 0 then

%p        R:= R,x;

%p        count:= count+1;

%p     fi

%p od od:

%p R;

%Y Cf. A004086.

%K nonn,base

%O 1,2

%A _Robert Israel_, May 21 2024