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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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..18.

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,more

AUTHOR

Brad Clardy, Dec 25 2014

STATUS

approved

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Last modified August 14 18:13 EDT 2022. Contains 356122 sequences. (Running on oeis4.)