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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 3 18:19 EST 2021. Contains 349467 sequences. (Running on oeis4.)