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%I A323234 #9 Jan 08 2019 19:08:03
%S A323234 1,2,3,2,4,5,6,2,4,7,8,9,10,11,12,2,4,7,8,13,14,15,16,17,18,19,20,21,
%T A323234 22,23,24,2,4,7,8,13,14,15,16,25,26,27,28,29,30,31,32,33,34,35,36,37,
%U A323234 38,39,40,41,42,43,44,45,46,47,48,2,4,7,8,13,14,15,16,25,26,27,28,29,30,31,32,49,50,51,52,53,54,55,56,57,58,59,60,61
%N A323234 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(1) = 0, and for n > 1, f(n) = ordered pair [A053645(n), A079944(n-2)], where A053645(n) gives n without its most significant bit, while A079944(n-2) gives the second most significant bit of n.
%C A323234 Also the restricted growth sequence transform of function f(1) = 0, f(n) = [A053645(n), A278222(n)] for n > 1.
%C A323234 For all i, j:
%C A323234   a(i) = a(j) => A286622(i) = A286622(j),
%C A323234   a(i) = a(j) => A323235(i) = A323235(j),
%C A323234   a(i) = a(j) => A323236(i) = A323236(j).
%H A323234 Antti Karttunen, <a href="/A323234/b323234.txt">Table of n, a(n) for n = 1..65537</a>
%H A323234 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%o A323234 (PARI)
%o A323234 up_to = 65537;
%o A323234 rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
%o A323234 A053644(n) = { my(k=1); while(k<=n, k<<=1); (k>>1); }; \\ From A053644
%o A323234 A053645(n) = (n-A053644(n));
%o A323234 A079944off0(n) = (1==binary(2+n)[2]);
%o A323234 A323234aux(n) = if(1==n,0,[A053645(n), A079944off0(n-2)]);
%o A323234 v323234 = rgs_transform(vector(up_to,n,A323234aux(n)));
%o A323234 A323234(n) = v323234[n];
%Y A323234 Cf. A053645, A079944, A278222, A286622, A323235, A323236.
%Y A323234 Cf. also A300226 (an analogous filter sequence for prime factorization).
%K A323234 nonn,base
%O A323234 1,2
%A A323234 _Antti Karttunen_, Jan 08 2019

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