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A252944 Fermat pseudoprimes that are not Carmichael numbers and have only composite XOR couples as defined in A182108.

%I A252944 #11 Sep 08 2022 08:46:10
%S A252944 23377,31417,49981,74665,220729,435671,679729,769757,852481,915981,
%T A252944 1016801,1023121,1128121,1397419,2008597,2987167,3073357,4014361
%N A252944 Fermat pseudoprimes that are not Carmichael numbers and have only composite XOR couples as defined in A182108.
%C A252944 There are 433 Fermat pseudoprimes that aren't Carmichael numbers below 2^22, but only 18 have this property. Carmichael numbers that have this property are in A182116.
%o A252944 (Magma)
%o A252944 function IsClardynum(X, i)
%o A252944   if i eq 1 then
%o A252944     return true;
%o A252944   else
%o A252944     xornum:=2^i - 2;
%o A252944     xorcouple:=BitwiseXor(X, xornum);
%o A252944     if (IsPrime(xorcouple)) then
%o A252944        return false;
%o A252944     else
%o A252944        return IsClardynum(X, i-1);
%o A252944     end if;
%o A252944   end if;
%o A252944 end function;
%o A252944 for n:= 3 to 1052503 by 2 do
%o A252944   if (IsOne(2^(n-1) mod n)
%o A252944       and not IsPrime(n)
%o A252944       and not n mod CarmichaelLambda(n) eq 1
%o A252944       and IsClardynum(n,Ilog2(n)))
%o A252944       then n;
%o A252944   end if;
%o A252944 end for;
%Y A252944 Cf. A153508, A001567, A252943, A182108, A182116.
%K A252944 nonn,more
%O A252944 1,1
%A A252944 _Brad Clardy_, Dec 25 2014