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A383284 Lexicographically earliest infinite sequence such that a(i) = a(j) => A265576(i) = A265576(j), for all i, j >= 1, where A265576 is the LCM-transform of EKG-sequence.

%I A383284 #12 Apr 22 2025 09:09:42
%S A383284 1,2,2,3,1,3,1,2,4,1,1,1,5,1,1,1,2,1,6,1,1,3,1,4,1,1,7,1,1,1,2,8,1,1,
%T A383284 1,9,1,1,1,1,1,10,1,1,1,1,1,1,1,5,1,1,1,1,1,11,1,1,1,12,1,1,1,2,1,13,
%U A383284 1,1,1,1,1,1,14,1,1,3,1,1,1,15,1,1,1,1,1,1,1,16,1,1,1,1,1,1,1,1,1,1,17
%N A383284 Lexicographically earliest infinite sequence such that a(i) = a(j) => A265576(i) = A265576(j), for all i, j >= 1, where A265576 is the LCM-transform of EKG-sequence.
%C A383284 Restricted growth sequence transform of A265576.
%H A383284 Antti Karttunen, <a href="/A383284/b383284.txt">Table of n, a(n) for n = 1..100000</a>
%H A383284 <a href="/index/Ed#EKG">Index entries for sequences related to EKG sequence</a>.
%F A383284 a(n) = 1+A000720(A265576(n)). [Conjectured. True if there are no composites in A265576]
%o A383284 (PARI)
%o A383284 up_to = 100000;
%o A383284 LCMtransform(v) = { my(len = length(v), b = vector(len), g = vector(len)); b[1] = g[1] = 1; for(n=2, len, g[n] = lcm(g[n-1], v[n]); b[n] = g[n]/g[n-1]); (b); };
%o A383284 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 A383284 v064413 = readvec("b064413_huge_to.txt"); \\ From b-file of A064413 computed previously.
%o A383284 A064413(n) = v064413[n];
%o A383284 v383284 = rgs_transform(LCMtransform(vector(up_to, i, A064413(i))));
%o A383284 A383284(n) = v383284[n];
%Y A383284 Cf. A000720, A064413, A265576, A383285 (positions of terms > 1).
%Y A383284 Positions of records: {2} U A064423.
%K A383284 nonn
%O A383284 1,2
%A A383284 _Antti Karttunen_, Apr 22 2025