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%I #16 May 08 2021 23:06:05
%S 0,0,0,6,0,14,14,14,0,30,30,30,30,30,18,16,0,62,62,62,62,62,50,48,62,
%T 62,34,32,34,32,44,44,0,126,126,126,126,126,114,112,126,126,98,96,98,
%U 96,108,108,126,126,66,64,66,64,76,76,66,64,92,92,92,92,92,82,0,254,254,254,254,254,242,240,254,254,226,224,226,224,236,236,254,254,194,192,194
%N a(n) = A005187(n) XOR A006068(n), where XOR is bitwise-xor (A003987).
%H Antti Karttunen, <a href="/A283999/b283999.txt">Table of n, a(n) for n = 0..8192</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F a(n) = A005187(n) XOR A006068(n), where XOR is bitwise-xor (A003987).
%F a(n) = A006068(2*n) XOR A283997(2*n).
%t Table[BitXor[Fold[BitXor, n, Quotient[n, 2^Range[BitLength@ n - 1]]], 2 n - DigitCount[2 n, 2, 1]], {n, 0, 84}] (* _Michael De Vlieger_, Mar 20 2017, after _Jan Mangaldan_ at A006068 *)
%o (Scheme) (define (A283999 n) (A003987bi (A005187 n) (A006068 n))) ;; Where A003987bi implements bitwise-XOR (A003987).
%o (PARI) b(n) = if(n<1, 0, b(n\2) + n%2);
%o A(n) = 2*n - b(2*n);
%o a(n) = if(n<2, n, 2*a(floor(n/2)) + (n%2 + a(floor(n/2))%2)%2);
%o for(n=0, 110, print1(bitxor(A(n),a(n)),", ")) \\ _Indranil Ghosh_, Mar 25 2017
%o (Python)
%o def A(n): return 2*n - bin(2*n)[2:].count("1")
%o def a(n): return n if n<2 else 2*a(n//2) + (n%2 + a(n//2)%2)%2
%o print([A(n)^a(n) for n in range(111)]) # _Indranil Ghosh_, Mar 25 2017
%Y Cf. A003987, A005187, A006068, A283997.
%K nonn,base
%O 0,4
%A _Antti Karttunen_, Mar 20 2017
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