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A371944 The binary expansion of a(n) corresponds to the ordinal transform (reduced modulo 2) of the binary expansion of n.

%I A371944 #16 Apr 17 2024 04:13:50
%S A371944 0,1,3,2,6,6,5,5,13,12,12,13,10,11,11,10,26,26,25,25,25,25,26,26,21,
%T A371944 21,22,22,22,22,21,21,53,52,52,53,50,51,51,50,50,51,51,50,53,52,52,53,
%U A371944 42,43,43,42,45,44,44,45,45,44,44,45,42,43,43,42,106,106
%N A371944 The binary expansion of a(n) corresponds to the ordinal transform (reduced modulo 2) of the binary expansion of n.
%C A371944 Leading zeros are ignored.
%C A371944 All terms belong to A063037.
%H A371944 Rémy Sigrist, <a href="/A371944/b371944.txt">Table of n, a(n) for n = 0..8191</a>
%H A371944 OEIS Wiki, <a href="/wiki/Ordinal_transform">Ordinal transform</a>
%H A371944 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A371944 A070939(a(n)) = A070939(n).
%F A371944 a(floor(n/2)) = floor(a(n)/2).
%e A371944 For n = 43: the binary expansion of 43 is "101011", the corresponding ordinal transform is "1, 1, 2, 2, 3, 4", reducing modulo 2 yields "110010", the binary expansion of a(43), so a(43) = 50.
%t A371944 {0}~Join~Array[(c[0] = 1; c[1] = 1; FromDigits[Map[Mod[c[#]++, 2] &, IntegerDigits[#, 2] ], 2]) &, 120] (* _Michael De Vlieger_, Apr 16 2024 *)
%o A371944 (PARI) a(n) = { my (b = binary(n), f = vector(2)); for (i = 1, #b, b[i] = f[1+b[i]]++;); fromdigits(b % 2, 2); }
%Y A371944 Cf. A063037, A070939, A371961.
%K A371944 nonn,base
%O A371944 0,3
%A A371944 _Rémy Sigrist_, Apr 13 2024