A214643 Primes p such that p XOR 22 = p + 22.

41, 73, 97, 137, 193, 233, 257, 353, 449, 457, 521, 577, 617, 641, 673, 769, 809, 929, 937, 1033, 1097, 1129, 1153, 1193, 1217, 1249, 1289, 1321, 1409, 1481, 1601, 1609, 1697, 1801, 1889, 1993, 2017, 2081, 2089, 2113, 2153, 2273, 2281, 2377, 2441, 2473, 2593

Offset

1,1

Comments

It seems that all of the terms in A197918 with the exception of the first three terms are also in this sequence.

Links

Table of n, a(n) for n=1..47.

Mathematica

Select[Range[3000], PrimeQ[#] && BitXor[#, 22] == # + 22 &] (* T. D. Noe, Jul 24 2012 *)
Select[Prime[Range[400]], BitXor[#, 22]==#+22&] (* Harvey P. Dale, Jul 23 2023 *)

Prog

(Magma)
XOR := func<a, b | Seqint([ (adigs[i] + bdigs[i]) mod 2 : i in [1..n]], 2)
                       where adigs := Intseq(a, 2, n)
                       where bdigs := Intseq(b, 2, n)
                       where n := 1 + Ilog2(Max([a, b, 1]))>;
m:=22;
  for n in [2 .. 10000] do
     if IsPrime(n)  then  pn:=n;
        if (XOR(pn, m) eq pn+m) then pn; end if;
     end if;
  end for;

Crossrefs

Cf. A197918.

Sequence in context: A057540 A362592 A105126 * A142038 A213047 A269426

Adjacent sequences: A214640 A214641 A214642 * A214644 A214645 A214646

Keyword

nonn

Author

Brad Clardy, Jul 23 2012

Status

approved