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 A243593 #36 Aug 11 2015 05:06:56
%S A243593 5,7,11,13,17,23,29,37,41,53,59,97,101,127,131,137,149,223,227,307,
%T A243593 331,337,347,349,419,541,547,557,563,569,587,809,821,967,1277,1361,
%U A243593 1367,1399,1409,1423,1427,1429,1433,1439,1447,1847,1861,1867,1871,1949,1973
%N A243593 Primes giving record values of f(n) = (2*Sum_{i=1..n}(i*prime(i)) / Sum_{i=1..n}(prime(i))-(n+1))/(n-1).
%C A243593 Is the sequence finite? It would mean that the value of f(n) would become monotonic after inclusion of the largest prime in the sequence.
%C A243593 It should be easy to prove that the value of lim 3*f(n) is 1 when n approaches infinity.
%C A243593 The generalized formula 3*(2*sum_XY/sum_Y - (n+1))/(n-1) is a non-linear correlation coefficient between the X (1,2,3...) and the nonnegative Y values, with range from -3 to +3, and linear correlation still giving value 1 or -1.
%C A243593 What is the next term after 32057?
%H A243593 Esko Ranta, <a href="/A243593/b243593.txt">Table of n, a(n) for n = 1..206</a>
%e A243593 3rd prime is 5, and f(3) > f(2) so 5 is included in the sequence.
%e A243593 Starting at n=2, the values of f(n) are: 1/5, 3/10, 1/3, 11/28, 81/205, 71/174, 31/77, 81/200, 485/1161, ...
%o A243593 (PARI) f(n) = (2*sum(i=1,n,i*prime(i))/sum(i=1, n, prime(i)) - (n+1))/(n-1);
%o A243593 lista(nn) = {last = f(2); for (i=3, nn, new = f(i); if (new > last, print1(prime(i), ", ");); new = last;);} \\ _Michel Marcus_, Jun 10 2014
%Y A243593 Cf. A000040, A014285, A007504, A046933, A014689, A000101.
%K A243593 nonn
%O A243593 1,1
%A A243593 _Esko Ranta_, Jun 07 2014