A055094 Binary encoding of quadratic residue set of n. L(1/n) is the most significant bit, L(n-1/n) is the least significant bit, i.e., the rows of A055088 interpreted as binary numbers.

0, 1, 2, 4, 9, 22, 52, 72, 146, 313, 738, 1156, 2829, 6772, 9520, 18496, 53643, 75154, 162438, 312328, 600116, 1513186, 4023888, 4737152, 9741609, 23182093, 38478994, 76286020, 166236537, 311977264, 921787428, 1212203072, 2962424994

Offset: 1

Author

Antti Karttunen, Apr 04 2000

Keywords

• nonn

Comments

L(a/n) stands for generalized Legendre symbol, with value = 1 only if a is a quadratic residue of n.

Crossrefs

Cf. A055088, A054432, A055095.

Programs

Maple

A055094 := proc(n)
    local i, z;
    z := 0;
    for i from 1 to n-1 do
        z := z*2;
        if (1 = numtheory[quadres](i, n)) then
            z := z + 1;
        fi;
    od;
    return z;
end proc:

Mathematica

a[n_] := With[{rr = Table[Mod[k^2, n], {k, 1, n - 1}] // Union}, Boole[ MemberQ[rr, #]]& /@ Range[n - 1]] // FromDigits[#, 2]&; Array[a, 40] (* Jean-François Alcover, Mar 05 2016*)

PARI

{a(n)=sum(k=1, n-1, 2^(k-1)*(0Michael Somos, Oct 14 2006 */

Sage

def A055094(n) :
    Q = quadratic_residues(n)
    z = 0
    for i in (1..n-1)  :
        z = z*2
        if i in Q : z += 1
    return z
[A055094(n) for n in (1..33)] # Peter Luschny, Aug 08 2012

Formula

a(n) = qrs2bincode(n)