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

1,3

Comments

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

Links

Table of n, a(n) for n=1..33.

Formula

a(n) = qrs2bincode(n)

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*)

Prog

(PARI) {a(n)=sum(k=1, n-1, 2^(k-1)*(0<sum(i=1, n-1, i^2%n==n-k)))} /* Michael 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

Crossrefs

Cf. A055088, A054432, A055095.

Sequence in context: A363771 A057580 A129875 * A369472 A055729 A317735

Adjacent sequences: A055091 A055092 A055093 * A055095 A055096 A055097

Keyword

nonn

Author

Antti Karttunen, Apr 04 2000

Status

approved