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A080117
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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.
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7
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2, 10, 52, 738, 2866, 53620, 162438, 4023888, 166243974, 921787428, 48034443442, 935251508324, 2558696229078, 68055676507664, 2655011787909270, 210067141980993186, 831463106366605026, 42882922858578320598
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OFFSET
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2,1
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LINKS
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FORMULA
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MAPLE
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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;
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MATHEMATICA
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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 *)
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PROG
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p = nth_prime(n)
return c if 3 == p%4 else A080261(c)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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