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 A237684 #27 Nov 07 2024 08:31:53
%S A237684 1,1,1,1,1,1,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%T A237684 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%U A237684 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
%N A237684 a(n) = floor(n*prime(n) / Sum_{i<=n} prime(i)).
%C A237684 a(n) = 1 for n = 8 and 1 <= n <= 6.
%C A237684 a(n) = 2 for n = 7 and 9 <= n < 10^11 (verified terms).
%C A237684 Conjectures:
%C A237684 (1): a(n) = 1 or 2 for all n.
%C A237684 (2): sequence of numbers n sorted by decreasing values of function f(n) = n*prime(n) / Sum_{i<=n} prime(i): 48, 35, 31, 25, 17, 49, 33, 69, 32, 26, 43, 38, 12, 63, 102, 67, 68, 37, ... The last term of this sequence is 1.
%C A237684 (3): maximal value of function f(n) is for n = 48: f(48) = 10704/4661 = 2.29650289637416...
%C A237684 (4): minimal value of function f(n) is for n = 1: f(1) = 1.
%H A237684 Jaroslav Krizek, <a href="/A237684/b237684.txt">Table of n, a(n) for n = 1..87</a>
%H A237684 Manuel Kauers and Christoph Koutschan, <a href="https://arxiv.org/abs/2303.02793">Some D-finite and some Possibly D-finite Sequences in the OEIS</a>, arXiv:2303.02793 [cs.SC], 2023, p. 4.
%F A237684 a(n) = floor(A033286(n) / A007504(n)).
%e A237684 a(8) = floor(8*prime(8) / Sum_{i<=8} prime(i)) = floor(8*19 / 77) = 1.
%t A237684 Block[{$MaxExtraPrecision = 1000, a, t = 0, nn = 120}, Do[(t += #; Set[a[i], Floor[i*#/t]]) &[Prime[i]], {i, nn}]; Array[a, nn] ] (* _Michael De Vlieger_, Mar 10 2023 *)
%Y A237684 Cf. A007504, A033286.
%K A237684 nonn
%O A237684 1,7
%A A237684 _Jaroslav Krizek_, Feb 21 2014