A252944 - OEIS

%I #11 Sep 08 2022 08:46:10

%S 23377,31417,49981,74665,220729,435671,679729,769757,852481,915981,

%T 1016801,1023121,1128121,1397419,2008597,2987167,3073357,4014361

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

%C 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 (Magma)

%o function IsClardynum(X, i)

%o   if i eq 1 then

%o     return true;

%o   else

%o     xornum:=2^i - 2;

%o     xorcouple:=BitwiseXor(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 n:= 3 to 1052503 by 2 do

%o   if (IsOne(2^(n-1) mod n)

%o       and not IsPrime(n)

%o       and not n mod CarmichaelLambda(n) eq 1

%o       and IsClardynum(n,Ilog2(n)))

%o       then n;

%o   end if;

%o end for;

%Y Cf. A153508, A001567, A252943, A182108, A182116.

%K nonn,more

%O 1,1

%A _Brad Clardy_, Dec 25 2014