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Search: id:A161623
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| A161623 |
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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. |
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1
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OFFSET
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1,1
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COMMENT
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This is a family of increasingly restrictive Andrica-like conjectures that all imply Legendre's conjecture.
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EXAMPLE
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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)).
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CROSSREFS
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Sequence in context: A097213 A110612 A161740 this_sequence A010946 A022625 A125465
Adjacent sequences: A161620 A161621 A161622 this_sequence A161624 A161625 A161626
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KEYWORD
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nonn
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AUTHOR
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Daniel Tisdale (daniel6874(AT)gmail.com), Jun 15 2009
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