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%I #19 Mar 05 2016 06:04:12
%S 0,1,2,4,9,22,52,72,146,313,738,1156,2829,6772,9520,18496,53643,75154,
%T 162438,312328,600116,1513186,4023888,4737152,9741609,23182093,
%U 38478994,76286020,166236537,311977264,921787428,1212203072,2962424994
%N 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.
%C L(a/n) stands for generalized Legendre symbol, with value = 1 only if a is a quadratic residue of n.
%F a(n) = qrs2bincode(n)
%p A055094 := proc(n)
%p local i, z;
%p z := 0;
%p for i from 1 to n-1 do
%p z := z*2;
%p if (1 = numtheory[quadres](i, n)) then
%p z := z + 1;
%p fi;
%p od;
%p return z;
%p end proc:
%t 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*)
%o (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 */
%o (Sage)
%o def A055094(n) :
%o Q = quadratic_residues(n)
%o z = 0
%o for i in (1..n-1) :
%o z = z*2
%o if i in Q : z += 1
%o return z
%o [A055094(n) for n in (1..33)] # _Peter Luschny_, Aug 08 2012
%Y Cf. A055088, A054432, A055095.
%K nonn
%O 1,3
%A _Antti Karttunen_, Apr 04 2000
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