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A365720 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365719(i) = A365719(j) for all i, j >= 0, where A365719(n) = A046523(A356867(1+n)).

%I A365720 #11 Sep 17 2023 11:25:14
%S A365720 1,2,2,2,3,4,4,5,3,2,4,4,3,6,6,6,7,6,4,6,8,5,9,9,10,11,5,2,4,4,4,6,8,
%T A365720 8,9,6,3,6,6,6,12,12,9,13,10,6,10,12,7,14,13,14,15,9,4,8,8,6,9,12,12,
%U A365720 13,12,5,12,9,9,16,16,13,17,14,10,14,18,11,19,17,20,21,7,2,4,4,4,6,8,8,9,6,4,8,8,6,12,12,12
%N A365720 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365719(i) = A365719(j) for all i, j >= 0, where A365719(n) = A046523(A356867(1+n)).
%C A365720 Restricted growth sequence transform of A365719.
%C A365720 For all i, j >= 0:
%C A365720   A365718(i) = A365718(j) => a(i) = a(j),
%C A365720   a(i) = a(j) => A365721(i) = A365721(j),
%C A365720   a(i) = a(j) => A365722(i) = A365722(j).
%H A365720 Antti Karttunen, <a href="/A365720/b365720.txt">Table of n, a(n) for n = 0..59049</a>
%o A365720 (PARI)
%o A365720 up_to = 59049; \\ = 3^10.
%o A365720 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 A365720 A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };
%o A365720 A356867list(up_to) = { my(v=vector(up_to),met=Map(),h=0,ak); for(i=1,#v,if(1==vecsum(digits(i,3)), v[i] = i; h = i, ak = v[i-h]; forprime(p=2,,if(3!=p && !mapisdefined(met,p*ak), v[i] = p*ak; break))); mapput(met,v[i],i)); (v); };
%o A365720 v365720 = rgs_transform(apply(A046523,A356867list(1+up_to)));
%o A365720 A365720(n) = v365720[1+n];
%Y A365720 Cf. A046523, A356867, A365718, A365720 (rgs-transform), A365721, A365722.
%Y A365720 Cf. also A286622.
%K A365720 nonn,look
%O A365720 0,2
%A A365720 _Antti Karttunen_, Sep 17 2023