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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.

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A191858 The greatest integer M for which there are no primes between M^(1+1/n) and (M+1)^(1+1/n).

Original entry on oeis.org

0, 1051, 6776941, 50904310155, 833954771945899
Offset: 1

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Author

Alexei Kourbatov, Jun 18 2011

Keywords

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.

Examples

			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.

Links

Crossrefs

Cf. A144140, A192870.
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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