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

23377, 31417, 49981, 74665, 220729, 435671, 679729, 769757, 852481, 915981, 1016801, 1023121, 1128121, 1397419, 2008597, 2987167, 3073357, 4014361, 4415251, 4613665, 4806061, 4835209, 4974971, 4984001, 5133201, 5176153, 5400489, 6242685, 6350941, 6631549, 6973057

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.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

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

Sequence in context: A205834 A184229 A153771 * A246891 A189656 A204074

Adjacent sequences: A252941 A252942 A252943 * A252945 A252946 A252947

Keyword

nonn

Author

Brad Clardy, Dec 25 2014

Extensions

a(19) onwards from Amiram Eldar, Feb 07 2026

Status

approved