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%I A331300 #11 Jan 18 2020 18:23:10
%S A331300 1,2,3,4,5,6,7,8,9,10,11,12,13,12,14,15,16,17,18,19,20,21,22,23,24,19,
%T A331300 22,25,26,23,27,28,29,30,31,32,33,34,35,36,37,34,38,39,40,41,42,43,44,
%U A331300 32,35,45,40,39,46,47,48,36,42,47,49,43,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,57,62,69,70,71,72,73,74,65,75,76,77,78,79,80,81,55,58,82,64,69,83,84,74,63
%N A331300 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = min(n, A057889(n)), and A057889 is a bijective base-2 reverse.
%C A331300 Restricted growth sequence transform of A331166. See comments in that sequence.
%H A331300 Antti Karttunen, <a href="/A331300/b331300.txt">Table of n, a(n) for n = 0..100000</a>
%H A331300 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%o A331300 (PARI)
%o A331300 up_to = 100000;
%o A331300 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 A331300 A030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2));
%o A331300 A057889(n) = if(!n,n,A030101(n/(2^valuation(n,2))) * (2^valuation(n, 2)));
%o A331300 A331166(n) = min(n, A057889(n));
%o A331300 v331300 = rgs_transform(vector(1+up_to,n,A331166(n-1)));
%o A331300 A331300(n) = v331300[1+n];
%o A331300 for(n=0,up_to,write("b331300.txt", n, " ", A331300(n)));
%Y A331300 Cf. A057889, A331166.
%Y A331300 Cf. also A324400, A331303, A305801, A305801, A305900, A295300 for other "top level" filtering sequences.
%K A331300 nonn,base
%O A331300 0,2
%A A331300 _Antti Karttunen_, Jan 18 2020

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