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A331743 Lexicographically earliest infinite sequence such that a(i) = a(j) => A002487(i) = A002487(j) and A323901(i) = A323901(j) for all i, j.

%I A331743 #14 Feb 05 2020 16:53:34
%S A331743 1,2,2,3,2,4,3,5,2,6,4,7,3,8,5,9,2,10,6,11,4,12,7,13,3,14,8,15,5,16,9,
%T A331743 17,2,18,10,19,6,20,11,21,4,22,12,23,7,24,13,25,3,26,14,27,8,28,15,29,
%U A331743 5,30,16,31,9,32,17,33,2,34,18,35,10,36,19,37,6,38,20,39,11,40,21,41,4,42,22,43,12,44,23,45,7,46,24,47,13,48,25,49,3,50,26,51,14,52,27,53,8,54
%N A331743 Lexicographically earliest infinite sequence such that a(i) = a(j) => A002487(i) = A002487(j) and A323901(i) = A323901(j) for all i, j.
%C A331743 Restricted growth sequence transform of the ordered pair [A002487(n), A002487(A163511(n))].
%C A331743 For all i, j:
%C A331743   a(i) = a(j) => A331748(i) = A331748(j),
%C A331743   a(i) = a(j) => A331749(i) = A331749(j).
%H A331743 Antti Karttunen, <a href="/A331743/b331743.txt">Table of n, a(n) for n = 0..65537</a>
%H A331743 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A331743 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%F A331743 a(2^n) = 2 for all n >= 0.
%o A331743 (PARI)
%o A331743 \\ Needs also code from A323901.
%o A331743 up_to = 65537;
%o A331743 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 A331743 Aux331743(n) = [A002487(n), A323901(n)];
%o A331743 v331743 = rgs_transform(vector(1+up_to, n, Aux331743(n-1)));
%o A331743 A331743(n) = v331743[1+n];
%Y A331743 Cf. A002487, A163511, A323901, A324400, A331742, A331744, A331748, A331749.
%Y A331743 Differs from A331745 for the first time at n=77, where a(77) = 40, while A331745(77) = 24.
%Y A331743 Differs from A103391(1+n) for the first time at n=191, where a(191) = 23, while A103391(192) = 97.
%K A331743 nonn
%O A331743 0,2
%A A331743 _Antti Karttunen_, Feb 05 2020