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 A344582 #25 Jun 03 2021 02:04:32
%S A344582 1,2,4,30,180,462,890,1532,3385,19871,29040,59257,66762,31545,597311,
%T A344582 1448751,1421021,1293698,12768473,2279181,147165284,118374763,
%U A344582 821495413,2618883054,2247521689,3145845927,7650216016,27357920380,22859974504,189924891289,78076882908,189573830057
%N A344582 a(n) is the least k such that there are exactly n primes between prime(k) + 1 and floor(prime(k + 1)^2/prime(k)) (inclusive) or 0 if no such k exists.
%C A344582 a(n) is the least k such that A228098(k) = n.
%e A344582 a(4) = 30 as there are exactly 4 primes between prime(30) + 1 = 114 and floor(prime(31)^2/prime(30)) = 142 namely the four primes 127, 131, 137 and 139.
%o A344582 (PARI) upto(n) = {my(i, p, q, res = vector(1)); i = 1; p = 2; forprime(q = 3, oo, u = q^2\p; t = 1; forprime(r = q + 1, u, t++); if(t > #res, res = concat(res, vector(t - #res))); if(res[t] == 0, res[t] = i; ); p = q; i++; if(i > n, return(res))); }
%Y A344582 Cf. A228098, A230777.
%K A344582 nonn
%O A344582 1,2
%A A344582 _David A. Corneth_, May 24 2021
%E A344582 a(24)-a(32) from _Martin Ehrenstein_, Jun 02 2021