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A351094 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351092(i) = A351092(j), for all i, j >= 1.

%I A351094 #11 Feb 01 2022 18:57:26
%S A351094 1,1,1,1,2,1,3,1,1,2,2,1,1,3,4,1,4,1,5,2,6,2,7,1,8,1,1,3,2,4,1,1,4,4,
%T A351094 9,1,1,5,1,2,2,6,3,2,8,7,7,1,6,8,10,1,8,1,11,3,12,2,13,4,14,1,15,1,11,
%U A351094 4,16,4,17,9,18,1,12,1,19,5,20,1,15,2,1,2,2,6,21,3,4,2,4,8,3,7,1,7,22,1,3,6,8,8
%N A351094 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351092(i) = A351092(j), for all i, j >= 1.
%C A351094 Restricted growth sequence transform of A351092.
%H A351094 Antti Karttunen, <a href="/A351094/b351094.txt">Table of n, a(n) for n = 1..20000</a>
%o A351094 (PARI)
%o A351094 up_to = 20000;
%o A351094 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 A351094 A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
%o A351094 A289814(n) = { my(d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); }; \\ From A289814
%o A351094 A351092(n) = { my(m=1); fordiv(n>>valuation(n,2),d,m *= A019565(A289814(d))); (m); };
%o A351094 v351094 = rgs_transform(vector(up_to, n, A351092(n)));
%o A351094 A351094(n) = v351094[n];
%Y A351094 Cf. A351090, A351092, A351093.
%K A351094 nonn,easy
%O A351094 1,5
%A A351094 _Antti Karttunen_, Jan 31 2022