|
Search: id:A055088
|
|
|
| A055088 |
|
Triangle of generalized Legendre symbols L(a/b), with 1's for quadratic residues and 0's for quadratic non-residues. |
|
+0
4
|
|
| 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0
(list; table; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
For every prime of the form 4k+1 (A002144) the row is symmetric and for every prime of the form 4k+3 (A002145) the row is "complementarily symmetric".
|
|
FORMULA
|
[seq(quadres_0_1_array(j), j=1..)]; (See Maple code below)
|
|
EXAMPLE
|
Terms are L(1/2); L(1/3), L(2/3); L(1/4), L(2/4), L(3/4); L(1/5), ... where L(a/b) is 1 if an integer c exists such that c^2 is congruent to a (mod b) and 0 otherwise.
E.g. the tenth row gives the quadratic residues and non-residues of 11 (see A011582) and the twelfth row gives the same information for 13 (A011583), with -1's replaced by zeros.
|
|
MAPLE
|
with(numtheory, quadres); quadres_0_1_array := (n) -> one_or_zero(quadres((n-((trinv(n-1)*(trinv(n-1)-1))/2)), (trinv(n-1)+1)));
|
|
CROSSREFS
|
Cf. A054431 for one_or_zero and trinv. Each row interpreted as a binary number: A055094.
Sequence in context: A033788 A033782 A033778 this_sequence A068427 A164057 A140820
Adjacent sequences: A055085 A055086 A055087 this_sequence A055089 A055090 A055091
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Antti Karttunen Apr 18 2000
|
|
|
Search completed in 0.002 seconds
|
