OFFSET
1,2
COMMENTS
Terms are conjectural, even under the Riemann Hypothesis.
(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.
(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.
LINKS
Thomas R. Nicely, First occurrence prime gaps [For local copy see A000101]
Tomás Oliveira e Silva, Gaps between consecutive primes
EXAMPLE
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.
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
Alexei Kourbatov, Jun 18 2011
STATUS
approved