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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 PROG (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; 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.)