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%I #15 Oct 28 2021 12:37:08
%S 0,1051,6776941,50904310155,833954771945899
%N The greatest integer M for which there are no primes between M^(1+1/n) and (M+1)^(1+1/n)
%C Terms are conjectural, even under the Riemann Hypothesis.
%C (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 (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 Thomas R. Nicely, <a href="https://faculty.lynchburg.edu/~nicely/gaps/gaplist.html">First occurrence prime gaps</a> [For local copy see A000101]
%H Tomás Oliveira e Silva, <a href="http://sweet.ua.pt/tos/gaps.html">Gaps between consecutive primes</a>
%e 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 Cf. A144140, A192870.
%K nonn,hard
%O 1,2
%A _Alexei Kourbatov_, Jun 18 2011