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%I #9 Dec 20 2021 05:27:12
%S 1,1,2,1,2,3,4,3,1,2,3,5,1,2,3,6,4,4,1,2,3,7,5,6,4,5,1,2,3,8,5,1,2,3,
%T 6,1,2,3,7,8,4,1,2,3,9,9,4,10,7,8,9,10,5,5,10,1,2,3,6,1,2,3,11,6,4,1,
%U 2,3,11,6,4,12,1,2,3,12,11,7,8,1,2,3,13,5,5,14,4,1,2,3,13,12,7,8,6,9,13,14,1,2,3,6,10,14,4
%N Ordinal transform of the largest prime factor of the n-th term of EKG-sequence.
%C Ordinal transform of A304733(n) = A006530(A064413(n)).
%H Antti Karttunen, <a href="/A304734/b304734.txt">Table of n, a(n) for n = 1..20090</a>
%H <a href="/index/Ed#EKG">Index entries for sequences related to EKG sequence</a>
%t terms = 105;
%t ekGrapher[s_List] := Block[{m = s[[-1]], k = 3}, While[MemberQ[s, k] || GCD[m, k] == 1, k++]; Append[s, k]];
%t A304733 = FactorInteger[#][[-1, 1]]& /@ Nest[ekGrapher, {1, 2}, terms];
%t b[_] = 0;
%t a[n_] := a[n] = With[{t = A304733[[n]]}, b[t] = b[t]+1];
%t Array[a, terms] (* _Jean-François Alcover_, Dec 20 2021, after _Robert G. Wilson v_ in A064413 *)
%o (PARI)
%o A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);
%o A304733(n) = A006530(A064413(n)); \\ Needs also code for A064413.
%o ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
%o v304734 = ordinal_transform(vector(65539,n,A304733(n)));
%o A304734(n) = v304734[n];
%Y Cf. A006530, A064413, A064741, A304733.
%Y Cf. also A078899.
%K nonn,look
%O 1,3
%A _Antti Karttunen_, May 18 2018
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