A304733 The largest prime factor of the n-th term of EKG-sequence: a(n) = A006530(A064413(n)).

1, 2, 2, 3, 3, 3, 3, 2, 5, 5, 5, 3, 7, 7, 7, 3, 2, 5, 11, 11, 11, 3, 5, 5, 7, 7, 13, 13, 13, 3, 2, 17, 17, 17, 7, 19, 19, 19, 5, 5, 11, 23, 23, 23, 3, 5, 13, 3, 7, 7, 7, 5, 11, 13, 7, 29, 29, 29, 11, 31, 31, 31, 3, 2, 17, 37, 37, 37, 5, 13, 19, 5, 41, 41, 41, 3, 7, 11, 11, 43, 43, 43, 5, 17, 19, 5, 23, 47, 47, 47, 3, 7, 13, 13, 17, 11, 7, 3, 53, 53, 53, 19

Offset: 1

Author

Antti Karttunen, May 18 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to EKG sequence

Crossrefs

Cf. A006530, A064413, A064741, A304734.

Cf. also A251103.

Programs

Mathematica

ekGrapher[s_List] := Block[{m = s[[-1]], k = 3}, While[MemberQ[s, k] || GCD[m, k] == 1, k++]; Append[s, k]];
FactorInteger[#][[-1, 1]]& /@ Nest[ekGrapher, {1, 2}, 100] (* 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 an implementation of A064413.

Formula

a(n) = A006530(A064413(n)).