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.

2, 10, 52, 738, 2866, 53620, 162438, 4023888, 166243974, 921787428, 48034443442, 935251508324, 2558696229078, 68055676507664, 2655011787909270, 210067141980993186, 831463106366605026, 42882922858578320598

Offset: 2

Author

Antti Karttunen, Feb 11 2003

Keywords

• nonn

Crossrefs

Cf. A080118, A080146, A080148.

Programs

Maple

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;

Mathematica

A055094[n_] := With[{rr = Table[Mod[k^2, n], {k, 1, n-1}] // Union}, Boole[ MemberQ[rr, #]] & /@ Range[n-1]] // FromDigits[#, 2]&;
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]];
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 *)

Sage

# uses[A080261]
def A080117(n) :
    p = nth_prime(n)
    c = A055094(p)
    return c if 3 == p%4 else A080261(c)
[A080117(n) for n in (2..19)] # Peter Luschny, Aug 09 2012

Formula

a(A080148(n)) = A080146(A080148(n))