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A324533 Lexicographically earliest positive sequence such that a(i) = a(j) => A002487(i) = A002487(j) and A278219(i) = A278219(j), for all i, j >= 0.

%I A324533 #6 Mar 05 2019 18:20:27
%S A324533 1,2,3,4,3,5,6,7,3,8,9,10,6,11,12,13,3,11,14,15,9,16,17,18,6,19,17,20,
%T A324533 12,15,21,22,3,23,24,25,14,26,27,28,9,29,30,31,17,32,33,34,6,35,27,36,
%U A324533 17,37,38,39,12,40,33,39,21,25,41,42,3,15,43,39,24,44,45,46,14,47,48,49,27,50,51,46,9,52,48,53,30,54,55,56,17,57,58,59,33,60,61,62,6
%N A324533 Lexicographically earliest positive sequence such that a(i) = a(j) => A002487(i) = A002487(j) and A278219(i) = A278219(j), for all i, j >= 0.
%C A324533 Restricted growth sequence transform of the ordered pair [A002487(n), A278219(n)].
%H A324533 Antti Karttunen, <a href="/A324533/b324533.txt">Table of n, a(n) for n = 0..65537</a>
%H A324533 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A324533 For n >= 1, a(2^n) = 3.
%o A324533 (PARI)
%o A324533 up_to = 65537;
%o A324533 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 A324533 A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
%o A324533 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
%o A324533 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
%o A324533 A003188(n) = bitxor(n, n>>1);
%o A324533 A278219(n) = A046523(A005940(1+A003188(n)));
%o A324533 Aux324533(n) = [A002487(n), A278219(n)];
%o A324533 v324533 = rgs_transform(vector(1+up_to,n,Aux324533(n-1)));
%o A324533 A324533(n) = v324533[1+n];
%Y A324533 Cf. A002487, A278219, A286619, A324400.
%Y A324533 Cf. also A323889 (compare the scatterplots).
%K A324533 nonn
%O A324533 0,2
%A A324533 _Antti Karttunen_, Mar 05 2019