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 A055088 Triangle of generalized Legendre symbols L(a/b), with 1's for quadratic residues and 0's for quadratic non-residues. 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; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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". LINKS 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))); MATHEMATICA row[n_] := With[{rr = Table[Mod[k^2, n + 1], {k, 1, n}] // Union}, Boole[ MemberQ[rr, #]]& /@ Range[n]]; Array[row, 14] // Flatten (* Jean-François Alcover, Mar 05 2016 *) PROG (Sage) def A055088_row(n) :     Q = quadratic_residues(n+1)     return [int(i in Q) for i in (1..n)] for n in (1..14) : A055088_row(n)  # Peter Luschny, Aug 08 2012 CROSSREFS Cf. A054431 for one_or_zero and trinv. Each row interpreted as a binary number: A055094. Sequence in context: A033788 A329680 A257234 * A266666 A068427 A190191 Adjacent sequences:  A055085 A055086 A055087 * A055089 A055090 A055091 KEYWORD nonn,tabl AUTHOR Antti Karttunen, Apr 18 2000 STATUS approved

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Last modified April 7 13:32 EDT 2020. Contains 333305 sequences. (Running on oeis4.)