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Primes p such that p XOR 22 = p + 22.
1

%I #8 Jul 23 2023 19:07:11

%S 41,73,97,137,193,233,257,353,449,457,521,577,617,641,673,769,809,929,

%T 937,1033,1097,1129,1153,1193,1217,1249,1289,1321,1409,1481,1601,1609,

%U 1697,1801,1889,1993,2017,2081,2089,2113,2153,2273,2281,2377,2441,2473,2593

%N Primes p such that p XOR 22 = p + 22.

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

%t Select[Range[3000], PrimeQ[#] && BitXor[#, 22] == # + 22 &] (* _T. D. Noe_, Jul 24 2012 *)

%t Select[Prime[Range[400]],BitXor[#,22]==#+22&] (* _Harvey P. Dale_, Jul 23 2023 *)

%o (Magma)

%o XOR := func<a, b | Seqint([ (adigs[i] + bdigs[i]) mod 2 : i in [1..n]], 2)

%o where adigs := Intseq(a, 2, n)

%o where bdigs := Intseq(b, 2, n)

%o where n := 1 + Ilog2(Max([a, b, 1]))>;

%o m:=22;

%o for n in [2 .. 10000] do

%o if IsPrime(n) then pn:=n;

%o if (XOR(pn,m) eq pn+m) then pn; end if;

%o end if;

%o end for;

%Y Cf. A197918.

%K nonn

%O 1,1

%A _Brad Clardy_, Jul 23 2012