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 A375530 #22 Oct 21 2024 11:23:31
%S A375530 1,3,30,4530,143650830,226991170700228730,
%T A375530 669824890486184912549321336826596430,
%U A375530 7627311526552103393330686732733999706332372434754669475019405844335259730
%N A375530 a(n) is the denominator of Sum_{k = 1..n} prime(k) / A375529(k).
%H A375530 Alois P. Heinz, <a href="/A375530/b375530.txt">Table of n, a(n) for n = 0..11</a>
%H A375530 N. J. A. Sloane, <a href="https://www.youtube.com/watch?v=3RAYoaKMckM">A Nasty Surprise in a Sequence and Other OEIS Stories</a>, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; <a href="https://sites.math.rutgers.edu/~zeilberg/expmath/sloane85BD.pdf">Slides</a> [Mentions this sequence]
%F A375530 a(n) = prime(n)*a(n-1)^2 + a(n-1), with a(0) = 1.
%e A375530 The first few fractions Sum_{k = 1..n} prime(k) / A375529(k) are 0/1, 2/3, 29/30, 4529/4530, 143650829/143650830, 226991170700228729/226991170700228730, ...
%p A375530 a:= proc(n) option remember; `if`(n=0, 1,
%p A375530 ithprime(n)*a(n-1)^2+a(n-1))
%p A375530 end:
%p A375530 seq(a(n), n=0..7); # _Alois P. Heinz_, Oct 21 2024
%Y A375530 Cf. A374663, A374983/A375516, A375529.
%K A375530 nonn,frac
%O A375530 0,2
%A A375530 _Rémy Sigrist_ and _N. J. A. Sloane_, Sep 04 2024
%E A375530 a(0)=1 prepended by _Alois P. Heinz_, Oct 21 2024