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 A323359 #17 Jun 24 2023 13:21:38
%S A323359 1,5,1,11,7,1,11,1,31,1,41,23,13,29,1,1,19,41,89,1,103,11,1,1,11,1,37,
%T A323359 1,41,43,181,1,1,23,1,1,1,1,1,131,17,281,97,43,311,23,83,1,353,1,17,1,
%U A323359 1,37,419,43,1,151,29,17,61,1,1,131,67,137,1,191,1,1,61,89
%N A323359 a(n) = b(n+1)/b(n) - 1 where b(1)=2 and b(k) = b(k-1) + lcm(floor(sqrt(k^3)), b(k-1)).
%C A323359 Conjectures:
%C A323359 1. This sequence consists only of 1's and primes.
%C A323359 2. Every odd prime of the form floor(sqrt(m^3)) is a term of this sequence.
%C A323359 3. At the first appearance of each prime of the form floor(sqrt(m^3)), it is the next prime after the largest prime that has already appeared.
%C A323359 Record values appear to be A291139(m), m > 1. - _Bill McEachen_, Jun 23 2023
%o A323359 (PARI) Generator(n)={b1=2;list=[]; for(k=2, n, b2=b1+lcm(sqrtint(k^3),b1); a=b2/b1-1; list=concat(list,a);b1=b2); return(list)}
%Y A323359 Cf. A135506, A008578, A323386, A323388, A291139.
%K A323359 nonn
%O A323359 1,2
%A A323359 _Pedja Terzic_, Jan 12 2019