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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^(n-1) - 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
Sequence in context: A175942 A181669 A362082 * A052940 A191304 A102444
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Mar 04 2019
EXTENSIONS
a(31)-a(36) from Giovanni Resta, Mar 05 2019
STATUS
approved

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Last modified April 14 07:58 EDT 2024. Contains 371655 sequences. (Running on oeis4.)