cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

23377, 31417, 49981, 74665, 220729, 435671, 679729, 769757, 852481, 915981, 1016801, 1023121, 1128121, 1397419, 2008597, 2987167, 3073357, 4014361
Offset: 1

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Author

Brad Clardy, Dec 25 2014

Keywords

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.

Crossrefs

Programs

  • 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;
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