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 A161846 #23 Feb 19 2021 10:41:05
%S A161846 5,16,6,44,54,76,84,108,122,120,166,182,184,234,192,260,264,294,304,
%T A161846 342,378,342,408,426,414,468,488,474,516,576,588,576,604,590,696,694,
%U A161846 728,694,756,828,774,776,870,862,852,1010,922,998,916,1020,1032,1110,1104
%N A161846 Numerator of the ratio (prime((n+1)^2) - prime(n^2))/prime(n).
%C A161846 Note that prime(n^2) = A011757(n) and prime(n) = A000040(n).
%C A161846 Conjecture: the sequence of fractions (prime((n+1)^2) - prime(n^2)) / prime(n) converges to 4. There are several "heuristic demonstrations" but no proofs.
%F A161846 a(n) = numerator((A011757(n+1) - A011757(n))/A000040(n)). - _Petros Hadjicostas_, May 13 2020
%e A161846 The first few fractions are 5/2, 16/3, 6/1, 44/7, 54/11, ...= A161846/A161847.
%p A161846 A161846 := proc(n) ( ithprime((n+1)^2)-ithprime(n^2))/ithprime(n) ; numer(%) ; end: seq(A161846(n),n=1..25) ; # _R. J. Mathar_, Jun 22 2009
%t A161846 Table[(Prime[(n+1)^2]-Prime[n^2])/Prime[n],{n,60}]//Numerator (* _Harvey P. Dale_, Oct 24 2017 *)
%o A161846 (PARI) a(n) = numerator((prime((n+1)^2) - prime(n^2))/prime(n)); \\ _Michel Marcus_, May 14 2020
%Y A161846 Cf. A000040, A011757, A161847 (denominators).
%K A161846 nonn,frac
%O A161846 1,1
%A A161846 _Daniel Tisdale_, Jun 20 2009
%E A161846 Extended by _Ray Chandler_, May 06 2010
%E A161846 Various sections edited by _Petros Hadjicostas_, May 13 2020