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 A161847 #15 Oct 07 2024 01:05:55 %S A161847 2,3,1,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89, %T A161847 97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179, %U A161847 181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277 %N A161847 Denominator of the ratio (prime((n+1)^2) - prime(n^2))/prime(n). %C A161847 Conjecture: the sequence (prime((n+1)^2) - prime(n^2))/prime(n) converges to 4. %F A161847 a(n) = denominator((A011757(n+1) - A011757(n))/A000040(n)). - _Petros Hadjicostas_, May 13 2020 %e A161847 The first few fractions are 5/2, 16/3, 6/1, 44/7, 54/11, ... = A161846/A161847. %o A161847 (PARI) a(n) = denominator((prime((n+1)^2) - prime(n^2))/prime(n)); \\ _Michel Marcus_, May 14 2020 %Y A161847 Cf. A000040, A011757, A161846 (numerators). %K A161847 nonn,frac %O A161847 1,1 %A A161847 _Daniel Tisdale_, Jun 20 2009 %E A161847 Keyword:frac added by _R. J. Mathar_, Jun 30 2009 %E A161847 Extended by _Ray Chandler_, May 06 2010 %E A161847 Various sections edited by _Petros Hadjicostas_, May 13 2020