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A351030 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351031(i) = A351031(j) and A351032(i) = A351032(j), for all i, j >= 1.

%I A351030 #10 Jan 29 2022 22:31:53
%S A351030 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,17,18,19,20,2,
%T A351030 21,2,22,23,24,23,25,2,26,27,28,2,29,2,30,31,32,2,33,34,35,36,37,2,38,
%U A351030 39,40,41,42,2,43,2,44,45,46,36,47,2,48,49,50,2,51,2,52,53,54,55,56,2,57,58,59,2,60,61,62
%N A351030 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351031(i) = A351031(j) and A351032(i) = A351032(j), for all i, j >= 1.
%C A351030 Restricted growth sequence transform of the ordered pair [A351031(n), A351032(n)], or equally, of the ordered pair [A351033(n), A351034(n)].
%C A351030 For all i, j: a(i) = a(j) => A349910(i) = A349910(j).
%H A351030 Antti Karttunen, <a href="/A351030/b351030.txt">Table of n, a(n) for n = 1..65537</a>
%H A351030 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%o A351030 (PARI)
%o A351030 up_to = 65537;
%o A351030 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 A351030 A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
%o A351030 A048673(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (1+factorback(f))/2; };
%o A351030 A289813(n) = { my(d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==1, 1, 0)), 2); };
%o A351030 A289814(n) = { my(d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); };
%o A351030 A291759(n) = A289814(A048673(n));
%o A351030 A304759(n) = A289813(A048673(n));
%o A351030 A351031(n) = { my(m=1); fordiv(n,d,if(d<n,m *= A019565(A304759(d)))); (m); };
%o A351030 A351032(n) = { my(m=1); fordiv(n,d,if(d<n,m *= A019565(A291759(d)))); (m); };
%o A351030 Aux351030(n) = [A351031(n),A351032(n)];
%o A351030 v351030 = rgs_transform(vector(up_to, n, Aux351030(n)));
%o A351030 A351030(n) = v351030[n];
%Y A351030 Cf. A019565, A048673, A289813, A289814, A291759, A304759, A351031, A351032 A351033, A351034.
%Y A351030 Cf. also A293226, A349910.
%K A351030 nonn
%O A351030 1,2
%A A351030 _Antti Karttunen_, Jan 29 2022