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A324390 Lexicographically earliest positive sequence such that a(i) = a(j) => A278219(i) = A278219(j) and A324386(i) = A324386(j), for all i, j >= 0.

%I A324390 #7 Feb 28 2019 18:54:40
%S A324390 1,2,3,2,3,4,5,2,6,7,8,4,5,9,10,2,3,7,11,7,8,12,13,4,14,15,16,9,17,18,
%T A324390 14,2,6,7,19,20,11,21,22,7,23,24,25,26,27,28,27,4,14,29,30,15,31,32,
%U A324390 33,9,34,35,36,9,37,38,37,2,39,40,11,7,41,42,43,40,41,44,45,46,47,48,47,7,49,50,51,24,52,53,54,55,56,57,58,42,59,60,56,4,61,62,63
%N A324390 Lexicographically earliest positive sequence such that a(i) = a(j) => A278219(i) = A278219(j) and A324386(i) = A324386(j), for all i, j >= 0.
%C A324390 Restricted growth sequence transform of the ordered pair [A278219(n), A324386(n)].
%H A324390 Antti Karttunen, <a href="/A324390/b324390.txt">Table of n, a(n) for n = 0..65537</a>
%H A324390 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A324390 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A324390 a(A000225(n)) = 2 for all n >= 1.
%o A324390 (PARI)
%o A324390 up_to = 65537;
%o A324390 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 A324390 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
%o A324390 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
%o A324390 A278222(n) = A046523(A005940(1+n));
%o A324390 A003188(n) = bitxor(n, n>>1);
%o A324390 A278219(n) = A278222(A003188(n));
%o A324390 Aux324390(n) = [A278219(n), A324386(n)]; \\ See code for A324386 in that entry.
%o A324390 v324390 = rgs_transform(vector(1+up_to,n,Aux324390(n-1)));
%o A324390 A324390(n) = v324390[1+n];
%Y A324390 Cf. A278219, A324386.
%Y A324390 Cf. also A286619, A324343, A324344, A324380 (compare the scatter-plots).
%K A324390 nonn
%O A324390 0,2
%A A324390 _Antti Karttunen_, Feb 27 2019