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A161623 Greatest n for which the Andrica-like conjectural inequalities, Prime[n+1]-Prime[n]-(1/k)*Sqrt[Prime[n] < 0, appear to fail to hold, for k = 1,2,3,4,..., based on empirical evidence. 0
30, 430, 3644, 4612 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is a family of increasingly restrictive Andrica-like conjectures that all imply Legendre's conjecture.

LINKS

Table of n, a(n) for n=1..4.

EXAMPLE

Example: For k = 1, one needs n > 30 for the inequality to obtain, and it is conjectured that it holds for all n > 30. In words, the first such inequality says that we expect to see a new prime p(n+1) between p(n) and p(n)+ Sqrt(p(n)).

CROSSREFS

Sequence in context: A110612 A290363 A161740 * A210431 A296919 A010946

Adjacent sequences:  A161620 A161621 A161622 * A161624 A161625 A161626

KEYWORD

nonn

AUTHOR

Daniel Tisdale, Jun 15 2009

STATUS

approved

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Last modified August 10 16:56 EDT 2020. Contains 336381 sequences. (Running on oeis4.)