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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

%I

%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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Last modified January 25 12:40 EST 2022. Contains 350572 sequences. (Running on oeis4.)