A055131 Those composite s for which A055095[s] = 2.

15, 39, 51, 87, 111, 123, 159, 183, 219, 267, 291, 303, 327, 339, 411, 447, 471, 519, 543, 579, 591, 687, 699, 723, 771, 807, 831, 843, 879, 939, 951, 1011, 1047, 1059, 1119, 1167, 1191, 1203, 1227, 1263, 1299, 1347, 1371, 1383, 1527, 1563, 1623, 1671

Offset: 0

Author

Antti Karttunen, Apr 04 2000

Keywords

• nonn

Programs

Maple

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;

Mathematica

A005811[n_] := Length[Length /@ Split[IntegerDigits[n, 2]]];
A055094[n_] := With[{rr = Table[Mod[k^2, n], {k, 1, n-1}] // Union}, Boole[MemberQ[rr, #]] & /@ Range[n-1]] // FromDigits[#, 2]&;
A055095[1] = 0; A055095[n_] := 2*A005811[A055094[n]] - (n-1);
A055131 = Position[Array[A055095, 2000], 2] // Flatten // Select[#, CompositeQ]& (* Jean-François Alcover, Mar 06 2016 *)

Formula

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

Extensions

More terms from James Sellers, Apr 21 2000