

A306662


Least number k such that the determinant of the circulant matrix of its representation in base 2 is equal to n.


2



0, 1, 5, 11, 23, 47, 95, 191, 43, 38, 1535, 3071, 571, 12287, 24575, 137, 269, 196607, 393215, 786431, 295, 687, 6291455, 12582911, 69, 155, 100663295, 134, 293, 805306367, 1610612735, 3221225471, 75, 518, 25769803775, 301, 8874
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


COMMENTS

Here only the least numbers are listed: e.g., a(10) = 1531, even if 1791, 1919, 1983, 2015, 2031, 2039, 2043, etc. also produce 10.
The sequence is infinite because any number of the form 3*2^(n1)  1 (A083329) has the determinant of the circulant matrix of its representation in base 2 equal to n but, in general, it is not the least possible term.
It would be nice to characterize the values of n where k < A083329(n).


LINKS



EXAMPLE

 1 0 1 1 
a(3) = 11 because 11 = 1011_2 and det  1 1 0 1  = 3
 1 1 1 0 
 0 1 1 1 
.
and 11 is the least number to have this property.
.
 1 0 1 1 1 
 1 1 0 1 1 
a(4) = 23 because 23 = 10111_2 and det  1 1 1 0 1  = 4
 1 1 1 1 0 
 0 1 1 1 1 
.
and 23 is the least number to have this property.


MAPLE

with(linalg): P:=proc(q) local a, b, c, d, j, k, i, n, t;
print(0); for i from 1 to q do for n from 1 to q do
a:=convert(n, base, 2); d:=nops(a); c:=[];
for k from 1 to nops(a) do c:=[op(c), a[k]]; od; t:=[op([]), c];
for k from 2 to d do b:=[op([]), c[nops(c)]];
for j from 1 to nops(c)1 do
b:=[op(b), c[j]]; od; c:=b; t:=[op(t), c]; od;
if i=det(t) then print(n); break; fi; od; od; end: P(10^7);


CROSSREFS



KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



