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

1,1

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.

Links

Table of n, a(n) for n=1..43.

Prog

(Magma)
XOR := func<a, b | Seqint([ (adigs[i] + bdigs[i]) mod 2 : i in [1..n]], 2)
    where adigs := Intseq(a, 2, n)
    where bdigs := Intseq(b, 2, n)
    where n := 1 + Ilog2(Max([a, b, 1]))>;
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;

Crossrefs

Cf. A199824.

Sequence in context: A087931 A044879 A060947 * A066697 A076338 A237620

Adjacent sequences: A182105 A182106 A182107 * A182109 A182110 A182111

Keyword

nonn

Author

Brad Clardy, Apr 12 2012

Status

approved