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%I #7 Sep 08 2022 08:45:54
%S 513,695,925,1177,1355,1395,1507,1681,1685,1687,1689,1819,1827,1893,
%T 1959,2043,2165,2169,2637,2651,2757,2875,2987,3159,3339,3417,3503,
%U 3649,3681,3743,3873,3963,3975,4041,4169,4353,4489,4767,4773,4805,4845,4881,5123
%N 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.
%C 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.
%o (Magma)
%o XOR := func<a, b | Seqint([ (adigs[i] + bdigs[i]) mod 2 : i in [1..n]], 2)
%o where adigs := Intseq(a, 2, n)
%o where bdigs := Intseq(b, 2, n)
%o where n := 1 + Ilog2(Max([a, b, 1]))>;
%o function IsClardynum(X,i)
%o if i eq 1 then
%o return true;
%o else
%o xornum:=2^i - 2;
%o xorcouple:=XOR(X,xornum);
%o if (IsPrime(xorcouple)) then
%o return false;
%o else
%o return IsClardynum(X,i-1);
%o end if;
%o end if;
%o end function;
%o for i:= 3 to 10001 by 2 do
%o if not IsPrime(i) then
%o if IsClardynum(i,Ilog2(i)) then i;
%o end if;
%o end if;
%o end for;
%Y Cf. A199824.
%K nonn
%O 1,1
%A _Brad Clardy_, Apr 12 2012
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