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A252944
Fermat pseudoprimes that are not Carmichael numbers and have only composite XOR couples as defined in A182108.
0
23377, 31417, 49981, 74665, 220729, 435671, 679729, 769757, 852481, 915981, 1016801, 1023121, 1128121, 1397419, 2008597, 2987167, 3073357, 4014361
OFFSET
1,1
COMMENTS
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.
PROG
(Magma)
function IsClardynum(X, i)
if i eq 1 then
return true;
else
xornum:=2^i - 2;
xorcouple:=BitwiseXor(X, xornum);
if (IsPrime(xorcouple)) then
return false;
else
return IsClardynum(X, i-1);
end if;
end if;
end function;
for n:= 3 to 1052503 by 2 do
if (IsOne(2^(n-1) mod n)
and not IsPrime(n)
and not n mod CarmichaelLambda(n) eq 1
and IsClardynum(n, Ilog2(n)))
then n;
end if;
end for;
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Brad Clardy, Dec 25 2014
STATUS
approved