This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A203555 #16 Mar 31 2012 10:28:36
%S A203555 2,2,4,4,5,19,19,19,19,19,19,19,19,19,19,19,19,19,19,20,21,43,43,43,
%T A203555 43,43,43,43,43,43,43,43,43,43,43,43,43,43,43,43,43,43,43,45,45,46,47,
%U A203555 68,68,68,68,68,68,68,68,68,68,68,68,68,68,68,68,68,68,68
%N A203555 a(n) is the index m that maximizes R_m / p_(2m).
%C A203555 The R_n is A104272 and p_n is A000040. The function eta_max allow one to take a value of eta(x) from A191228 and finds a(n). Then one can use A179196 to find the prime index value.
%C A203555 a(n) records on the value of the index, m, when the max value, Max(m>=n,R_m/p_(2*m)) for each n.
%C A203555 The function eta_max(n) can be defined in the following way: With a(n) = m so that eta_max(n) := Max(m>=n,R_m/p_(2*m)) for each n.
%C A203555 Because the ratio R_a(n)/p_{2a(n)} approaches 1 as n approaches infinity, and the absolute max is at a(2), we see that this ratio has local maximums at increasing values of n. This sequence removes the "dips" between the local maximums. The values of a(n) implies, for all i >= n, R_(i+1) < R_a(n)/p_(2*a(n))* R_i. Because of these implications, this sequence can be made into a program finding values of a(n) to a limit L.
%e A203555 For m=98, max n>98 (R_m/p_(2*m)) = R_98/p_196 = 1.196144174 < 6/5 = 1.2
%e A203555 For m=99, max n>99 (R_m/p_(2*m)) = R_107/p_214 = 1549/1307 = 1.178070899 < 2^(0.25)
%Y A203555 Cf. A104272, A000040, A182873, A191228, A179196.
%K A203555 nonn
%O A203555 1,1
%A A203555 _John W. Nicholson_, Jan 02 2012