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A214864 Numbers k such that k XOR 10 = k - 10.

%I A214864 #35 Oct 27 2024 20:29:29
%S A214864 10,11,14,15,26,27,30,31,42,43,46,47,58,59,62,63,74,75,78,79,90,91,94,
%T A214864 95,106,107,110,111,122,123,126,127,138,139,142,143,154,155,158,159,
%U A214864 170,171,174,175,186,187,190,191,202
%N A214864 Numbers k such that k XOR 10 = k - 10.
%H A214864 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A214864 a(n) = 4*n + 6 + (3*(-1)^n+1)/2 + 2*(-1)^((2*n-1+(-1)^n)/4) for n >= 0.
%F A214864 a(n) = A016825(n) + A216178(n-1) for n > 0.
%F A214864 G.f. x*(10+x+3*x^2+x^3+x^4) / ( (1+x)*(1+x^2)*(x-1)^2 ). - _R. J. Mathar_, Mar 10 2013
%F A214864 Numbers k such that k mod 16 is one of {10, 11, 14, 15}. - _Joerg Arndt_, Mar 15 2013
%F A214864 a(n) = 16*floor((n-1)/4) + ((n-1) mod 2) + 4*floor(((n-1) mod 4)/2) + 10. - _Gary Detlefs_, Oct 26 2013 [corrected by _Jason Yuen_, Oct 27 2024]
%t A214864 Select[Range[200], BitXor[#, 10] == # - 10 &] (* _Alonso del Arte_, Oct 26 2013 *)
%o A214864 (Magma)
%o A214864 XOR := func<a, b | Seqint([ (adigs[i] + bdigs[i]) mod 2 : i in [1..n]], 2)
%o A214864     where adigs := Intseq(a, 2, n)
%o A214864     where bdigs := Intseq(b, 2, n)
%o A214864     where n := 1 + Ilog2(Max([a, b, 1]))>;
%o A214864 m:=10;
%o A214864 for n in [1 .. 250] do
%o A214864 if (XOR(n, m) eq n-m) then n; end if;
%o A214864 end for;
%o A214864 (Python)
%o A214864 def A214864(n): return (10,11,14,15)[n-1&3]+((n-1&-4)<<2) # _Chai Wah Wu_, Jan 30 2023
%Y A214864 Cf. A214863, A016825, A216178.
%K A214864 nonn,easy
%O A214864 1,1
%A A214864 _Brad Clardy_, Mar 09 2013