A182108 Odd composite numbers in successive intervals [2^i +1 .. 2^(i+1) -1] i=1,2,3... such that there are only composite symmetric XOR couples in either the original interval or any recursively halved interval that contains them.

513, 695, 925, 1177, 1355, 1395, 1507, 1681, 1685, 1687, 1689, 1819, 1827, 1893, 1959, 2043, 2165, 2169, 2637, 2651, 2757, 2875, 2987, 3159, 3339, 3417, 3503, 3649, 3681, 3743, 3873, 3963, 3975, 4041, 4169, 4353, 4489, 4767, 4773, 4805, 4845, 4881, 5123

Offset: 1

Author

Brad Clardy, Apr 12 2012

Keywords

• nonn

Comments

The description of the process is outlined in A199824. Up to the interval that starts 2^10 there are only 109 of these numbers, while there are a mere 50 primes of the type in A199824.

Crossrefs

Cf. A199824.

Programs

Magma

XOR := func;
function IsClardynum(X,i)
  if i eq 1 then
    return true;
  else
    xornum:=2^i - 2;
    xorcouple:=XOR(X,xornum);
    if (IsPrime(xorcouple)) then
       return false;
    else
       return IsClardynum(X,i-1);
    end if;
  end if;
end function;
for i:= 3 to 10001 by 2 do
   if not IsPrime(i) then
      if IsClardynum(i,Ilog2(i)) then i;
      end if;
   end if;
end for;