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 A191858 #17 Jun 02 2025 04:10:50 %S A191858 0,1051,6776941,50904310155,833954771945899 %N A191858 The greatest integer M for which there are no primes between M^(1+1/n) and (M+1)^(1+1/n). %C A191858 Terms are conjectural, even under the Riemann Hypothesis. %C A191858 (1) The initial term a(1)=0 gives a simple restatement of Legendre's conjecture: There are no primes between 0^2 and 1^2, but there is a prime between m^2 and (m+1)^2 for m>0. %C A191858 (2) Lists of known maximum prime gaps and known first occurrences of prime gaps help verify the initial terms in this sequence. However, a lengthy computation would be needed for subsequent terms. %H A191858 Thomas R. Nicely, <a href="https://faculty.lynchburg.edu/~nicely/gaps/gaplist.html">First occurrence prime gaps</a> [For local copy see A000101] %H A191858 Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/gaps.html">Gaps between consecutive primes</a> %e A191858 The second term is a(2)=1051 because there are no primes between 1051^(3/2) and 1052^(3/2), but there is at least one prime between m^(3/2) and (m+1)^(3/2) for m>1051. %Y A191858 Cf. A144140, A192870. %K A191858 nonn,hard %O A191858 1,2 %A A191858 _Alexei Kourbatov_, Jun 18 2011