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A324344 Lexicographically earliest positive sequence such that a(i) = a(j) => A000120(i) = A000120(j) and A324342(i) = A324342(j), for all i, j >= 0.

%I A324344 #7 Feb 24 2019 17:52:23
%S A324344 1,2,2,3,2,3,4,5,2,3,4,6,7,8,9,10,2,3,4,11,4,11,12,13,14,15,16,17,18,
%T A324344 19,20,21,2,3,4,11,22,11,15,19,14,23,24,25,26,13,10,27,28,29,30,31,32,
%U A324344 33,34,35,36,37,38,39,40,41,42,43,2,3,4,11,44,5,23,45,44,12,16,46,32,33,33,47,48,18,16,46,26,37,49,50,16,51,52,53,13,54,55,56,57,36,58,38,59,49,60
%N A324344 Lexicographically earliest positive sequence such that a(i) = a(j) => A000120(i) = A000120(j) and A324342(i) = A324342(j), for all i, j >= 0.
%C A324344 Restricted growth sequence transform of the ordered pair [A000120(n), A324342(n)].
%H A324344 Antti Karttunen, <a href="/A324344/b324344.txt">Table of n, a(n) for n = 0..65537</a>
%o A324344 (PARI)
%o A324344 up_to = 65537;
%o A324344 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 A324344 A002110(n) = prod(i=1,n,prime(i));
%o A324344 A030308(n,k) = bittest(n,k);
%o A324344 A283477(n) = prod(i=0,#binary(n),if(0==A030308(n,i),1,A030308(n,i)*A002110(1+i)));
%o A324344 A276150(n) = { my(s=0,m); forprime(p=2, , if(!n, return(s)); m = n%p; s += m; n = (n-m)/p); };
%o A324344 A324342(n) = A276150(A283477(n));
%o A324344 A324344aux(n) = [hammingweight(n), A324342(n)];
%o A324344 v324344 = rgs_transform(vector(1+up_to,n,A324344aux(n-1)));
%o A324344 A324344(n) = v324344[1+n];
%Y A324344 Cf. A000120, A324342, A324343.
%Y A324344 Cf. also A318310.
%K A324344 nonn
%O A324344 0,2
%A A324344 _Antti Karttunen_, Feb 24 2019