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%I #19 Sep 08 2022 08:46:02
%S 11,15,27,31,43,47,59,63,75,79,91,95,107,111,123,127,139,143,155,159,
%T 171,175,187,191,203,207,219,223,235,239,251,255,267,271,283,287,299,
%U 303,315,319,331,335,347,351,363
%N Numbers n such that n XOR 11 = n - 11.
%C Links to sequences of the form n XOR m = n - m are found below with the value of m specified.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F a(n)= 1+8*n-2*(-1)^n.
%F a(n)=A016825(n) + A168392(n) + for n>0.
%F G.f. x*(11+4*x+x^2) / ( (1+x)*(x-1)^2 ). - _R. J. Mathar_, Mar 10 2013
%t Select[Range[400],BitXor[#,11]==#-11&] (* or *) LinearRecurrence[{1,1,-1},{11,15,27},50] (* _Harvey P. Dale_, Jun 05 2021 *)
%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:=11;
%o for n in [1 .. 500] do
%o if (XOR(n, m) eq n-m) then n; end if;
%o end for;
%Y Cf. A005408 (m=1), A042964 (m=2), A131098 (m=3), A047566 (m=4), A047550 (m=5), A047589 (m=6), A004771 (m=7), A115419 (m=8), A214865 (m=9), A214864 (m=10), A133894 (m=12), A125169 (m=15).
%Y Cf. also A016825, A168392.
%K nonn,easy
%O 1,1
%A _Brad Clardy_, Mar 09 2013
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