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Those composite s for which A055095[s] = 2.
2

%I #8 Mar 06 2016 10:53:40

%S 15,39,51,87,111,123,159,183,219,267,291,303,327,339,411,447,471,519,

%T 543,579,591,687,699,723,771,807,831,843,879,939,951,1011,1047,1059,

%U 1119,1167,1191,1203,1227,1263,1299,1347,1371,1383,1527,1563,1623,1671

%N Those composite s for which A055095[s] = 2.

%F a(n) = 3*((4*A005098[n])+1) = 3*A002144[n] ??? (Conjecture, not yet proved)

%p find_A055095_is_2_composites := proc(upto_n) local j,a; a := []; for j from 1 to upto_n do if(-1 = (j - wt(GrayCode(qrs2bincode((2*j)+1))))) then if(not isprime((2*j)+1)) then a := [op(a),((2*j)+1)]; fi; fi; od; RETURN(a); end;

%t A005811[n_] := Length[Length /@ Split[IntegerDigits[n, 2]]];

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

%t A055095[1] = 0; A055095[n_] := 2*A005811[A055094[n]] - (n-1);

%t A055131 = Position[Array[A055095, 2000], 2] // Flatten // Select[#, CompositeQ]& (* _Jean-François Alcover_, Mar 06 2016 *)

%K nonn

%O 0,1

%A _Antti Karttunen_, Apr 04 2000

%E More terms from _James A. Sellers_, Apr 21 2000