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A331303 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = min(n, A263273(n)), and A263273 is bijective base-3 reverse.

%I A331303 #6 Jan 18 2020 18:23:39
%S A331303 1,2,3,4,5,6,7,6,8,9,10,11,12,13,14,15,16,17,18,11,19,15,14,20,21,17,
%T A331303 22,23,24,25,26,27,28,29,30,31,32,27,33,34,35,36,37,38,39,40,30,41,42,
%U A331303 38,43,44,45,46,47,25,48,29,33,49,50,41,51,40,28,49,37,36,52,53,43,54,55,31,51,44,39,54,56,46,57,58,59,60,61,62,63,64,65,66,67,68,69
%N A331303 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = min(n, A263273(n)), and A263273 is bijective base-3 reverse.
%C A331303 Restricted growth sequence transform of A331173. See comments in that sequence.
%H A331303 Antti Karttunen, <a href="/A331303/b331303.txt">Table of n, a(n) for n = 0..100000</a>
%o A331303 (PARI)
%o A331303 up_to = 100000;
%o A331303 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 A331303 A030102(n) = { my(r=[n%3]); while(0<n\=3, r=concat(n%3, r)); subst(Polrev(r),x,3); };
%o A331303 A263273 = n -> if(!n,n,A030102(n/(3^valuation(n,3))) * (3^valuation(n, 3)));
%o A331303 A331173(n) = min(n, A263273(n));
%o A331303 v331303 = rgs_transform(vector(1+up_to,n,A331173(n-1)));
%o A331303 A331303(n) = v331303[1+n];
%Y A331303 Cf. A263273, A331173.
%Y A331303 Cf. also A331300.
%K A331303 nonn,base
%O A331303 0,2
%A A331303 _Antti Karttunen_, Jan 18 2020