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 A379444 #13 Jan 24 2025 18:30:58 %S A379444 4,5,8,7,11,10,11,11,15,18,17,15,17,17,21,24,25,21,23,24,31,27,30,29, %T A379444 30,30,40,34,40,39,35,38,38,37,41,40,42,45,48,54,51,51,47,56,50,51,57, %U A379444 52,66,57,60,57,64,57,65,71,65,69,67,64,78,66,68,69,72,77,81 %N A379444 a(n) is the difference between the least prime > (n+1)^2 and the largest prime < n^2, divided by 2. %C A379444 2*a(n) would be the gap needed between consecutive primes to provide a counterexample to Legendre's conjecture that there is always a prime between n^2 and (n+1)^2. The gaps actually observed are significantly smaller; see A378904 for comparison. %H A379444 Hugo Pfoertner, <a href="/A379444/b379444.txt">Table of n, a(n) for n = 2..10000</a> %F A379444 a(n) = (A007491(n+1) - A053001(n))/2. %F A379444 a(n) >= n + 2. %t A379444 a[n_]:=(NextPrime[(n+1)^2] - NextPrime[n^2,-1])/2; Array[a,67,2] (* _Stefano Spezia_, Jan 24 2025 *) %o A379444 (PARI) a379444(n) = (nextprime((n+1)^2) - precprime(n^2))/2 %Y A379444 Cf. A001223, A007491, A053001, A058043, A350100, A378904. %K A379444 nonn,easy %O A379444 2,1 %A A379444 _Hugo Pfoertner_, Dec 23 2024