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A366280 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366279(i) = A366279(j) for all i, j >= 0.

%I A366280 #10 Oct 06 2023 21:24:17
%S A366280 1,2,3,2,4,3,5,2,6,4,7,5,7,3,5,2,8,6,9,7,10,7,11,5,9,4,7,5,7,3,5,2,12,
%T A366280 8,13,9,14,10,15,7,14,9,15,11,15,7,11,5,13,6,9,7,10,7,11,5,9,4,7,5,7,
%U A366280 3,5,2,16,12,17,13,18,14,19,9,20,14,21,15,21,10,15,7,18,13,19,15,21,15,22,11,19,9,15,11,15
%N A366280 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366279(i) = A366279(j) for all i, j >= 0.
%C A366280 Restricted growth sequence transform of A366279.
%C A366280 For all i, j >= 0, a(i) = a(j) => A290251(i) = A290251(j).
%H A366280 Antti Karttunen, <a href="/A366280/b366280.txt">Table of n, a(n) for n = 0..65537</a>
%o A366280 (PARI)
%o A366280 up_to = 65537;
%o A366280 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 A366280 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
%o A366280 A030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2));
%o A366280 A057889(n) = if(!n,n,A030101(n/(2^valuation(n,2))) * (2^valuation(n, 2)));
%o A366280 A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
%o A366280 A366275(n) = A163511(A057889(n));
%o A366280 A366279(n) = A046523(A366275(n));
%o A366280 v366280 = rgs_transform(vector(1+up_to,n,A366279(n-1)));
%o A366280 A366280(n) = v366280[1+n];
%Y A366280 Cf. A046523, A057889, A163511, A278531, A290251, A366275, A366279.
%Y A366280 Cf. also A286531, A286602, A366262.
%K A366280 nonn,look
%O A366280 0,2
%A A366280 _Antti Karttunen_, Oct 06 2023