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A080117 Binary encoding of quadratic residue set formed for n-th prime, coerced to "complementarily symmetric binary sequence" with A080261 if the prime is of the form 4k+1.

%I A080117 #18 Sep 20 2022 07:54:30
%S A080117 2,10,52,738,2866,53620,162438,4023888,166243974,921787428,
%T A080117 48034443442,935251508324,2558696229078,68055676507664,
%U A080117 2655011787909270,210067141980993186,831463106366605026,42882922858578320598
%N A080117 Binary encoding of quadratic residue set formed for n-th prime, coerced to "complementarily symmetric binary sequence" with A080261 if the prime is of the form 4k+1.
%F A080117 a(A080148(n)) = A080146(A080148(n))
%p A080117 with(numtheory,ithprime); A080117 := proc(n) local c,p; p := ithprime(n); c := A055094(p); if(3 = (p mod 4)) then RETURN(c); else RETURN(A080261(c)); fi; end;
%t A080117 A055094[n_] := With[{rr = Table[Mod[k^2, n], {k, 1, n-1}] // Union}, Boole[ MemberQ[rr, #]] & /@ Range[n-1]] // FromDigits[#, 2]&;
%t A080117 A080261[n_] := Module[{bb = IntegerDigits[n, 2]}, lg = Length[bb]; Do[ bb[[i]] = 1 - bb[[i]], {i, lg, lg - Floor[lg/2] + 1, -1}]; FromDigits[ bb, 2]];
%t A080117 a[n_] := Module[{c, p = Prime[n]}, c = A055094[p]; If[Mod[p, 4] == 3, c, A080261[c]]]; Table[a[n], {n, 2, 20}] (* _Jean-François Alcover_, Mar 05 2016, adapted from Maple *)
%o A080117 (Sage) # uses[A080261]
%o A080117 def A080117(n) :
%o A080117     p = nth_prime(n)
%o A080117     c = A055094(p)
%o A080117     return c if 3 == p%4 else A080261(c)
%o A080117 [A080117(n) for n in (2..19)] # _Peter Luschny_, Aug 09 2012
%Y A080117 Cf. A080118, A080146, A080148.
%K A080117 nonn
%O A080117 2,1
%A A080117 _Antti Karttunen_, Feb 11 2003