A304734 Ordinal transform of the largest prime factor of the n-th term of EKG-sequence.

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, 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, 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

Offset: 1

Author

Antti Karttunen, May 18 2018

Keywords

• nonn
• look

Comments

Ordinal transform of A304733(n) = A006530(A064413(n)).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20090
• Index entries for sequences related to EKG sequence

Crossrefs

Cf. A006530, A064413, A064741, A304733.

Cf. also A078899.

Programs

Mathematica

terms = 105;
ekGrapher[s_List] := Block[{m = s[[-1]], k = 3}, While[MemberQ[s, k] || GCD[m, k] == 1, k++]; Append[s, k]];
A304733 = FactorInteger[#][[-1, 1]]& /@ Nest[ekGrapher, {1, 2}, terms];
b[_] = 0;
a[n_] := a[n] = With[{t = A304733[[n]]}, b[t] = b[t]+1];
Array[a, terms] (* Jean-François Alcover, Dec 20 2021, after Robert G. Wilson v in A064413 *)

PARI

A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);
A304733(n) = A006530(A064413(n)); \\ Needs also code for A064413.
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; };
v304734 = ordinal_transform(vector(65539,n,A304733(n)));
A304734(n) = v304734[n];