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 A349999 #13 Dec 17 2024 12:58:03 %S A349999 2,3,4,5,6,7,8,9,10,11,12,13,16,18,19,22,24,26,27,28,29,30,32,33,35, %T A349999 36,38,39,40,41,44,45,47,51,54,56,63,65,68,70,71,78,80,85,94,99,106, %U A349999 107,114,115,120,121,127,133,138,146,154,155,164,168,169,175,176,177 %N A349999 Least number m of primes that must have appeared in an interval [j^2, (j+1)^2], such that all intervals [k^2, (k+1)^2], k>j contain more than m primes. The corresponding values of j are A349998. %C A349999 All terms are empirical (see the graph of A014085 for the limited width of the scatter band), but supporting the validity of Legendre's conjecture that there is always a prime between n^2 and (n+1)^2. %C A349999 The terms are determined by searching from large to small indices in A014085 for new minima. %H A349999 Hugo Pfoertner, <a href="/A349999/b349999.txt">Table of n, a(n) for n = 1..2414</a> %F A349999 a(n) = A014085(A349998(n)). %F A349999 A014085(k) > a(n) for k > A349998(n). %F A349999 A014085(k) >= a(n) for k >= A349997(n). %e A349999 See A349997 and A349998. %Y A349999 Cf. A014085, A084597, A349997, A349998. %Y A349999 Cf. A333846, A349996. %K A349999 nonn %O A349999 1,1 %A A349999 _Hugo Pfoertner_, Dec 09 2021