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A365388 Lexicographically earliest infinite sequence such that a(i) = a(j) => A334867(i) = A334867(i) and A365386(j) = A365386(j) for all i, j >= 1.

%I A365388 #10 Sep 07 2023 16:09:57
%S A365388 1,1,2,1,3,2,4,1,5,3,6,2,7,4,8,1,9,5,10,3,11,6,12,2,13,7,14,4,15,8,16,
%T A365388 1,17,9,18,5,19,10,20,3,21,11,22,6,23,12,24,2,25,13,26,7,27,14,28,4,
%U A365388 29,15,30,8,31,16,32,1,33,17,34,9,35,18,36,5,37,19,38,10,39,20,40,3,41,21,42,11,43,22,44,6,45,23,46,12,47,24,48,2,49,25,41
%N A365388 Lexicographically earliest infinite sequence such that a(i) = a(j) => A334867(i) = A334867(i) and A365386(j) = A365386(j) for all i, j >= 1.
%C A365388 Restricted growth sequence transform of the ordered pair [A334867(n), A365386(n)], or equally, of the quadruplet [A329697(n), A334204(n), A331410(n), A365385(n)].
%C A365388 For all i, j:
%C A365388   A003602(i) = A003602(j) => a(i) = a(j),
%C A365388   a(i) = a(j) => A334867(i) = A334867(j),
%C A365388   a(i) = a(j) => A335880(i) = A335880(j),
%C A365388   a(i) = a(j) => A365386(i) = A365386(j).
%H A365388 Antti Karttunen, <a href="/A365388/b365388.txt">Table of n, a(n) for n = 1..65537</a>
%o A365388 (PARI)
%o A365388 up_to = 65537;
%o A365388 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 A365388 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 A365388 A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
%o A365388 A334204(n) = A329697(A163511(n));
%o A365388 A331410(n) = if(!bitand(n,n-1),0,1+A331410(n+(n/vecmax(factor(n)[, 1]))));
%o A365388 A365385(n) = A331410(A163511(n));
%o A365388 A365388aux(n) = [A329697(n),A334204(n),A331410(n),A365385(n)];
%o A365388 v365388 = rgs_transform(vector(up_to,n,A365388aux(n)));
%o A365388 A365388(n) = v365388[n];
%Y A365388 Cf. A163511, A329697, A331410, A334204, A334867, A335880, A365385, A365386.
%Y A365388 Differs from A003602 and A351090 for the first time at n=99, where a(99) = 41, while A003602(99) = A351090(99) = 50.
%K A365388 nonn
%O A365388 1,3
%A A365388 _Antti Karttunen_, Sep 07 2023