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Search: id:A074976
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| A074976 |
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Round(1/(sqrt(p(n+1))-sqrt(p(n))) where p(n) denotes the n-th prime. |
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3
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| 3, 2, 2, 1, 3, 2, 4, 2, 2, 5, 2, 3, 6, 3, 2, 2, 8, 3, 4, 8, 3, 4, 3, 2, 5, 10, 5, 10, 5, 2, 6, 4, 12, 2, 12, 4, 4, 6, 4, 4, 13, 3, 14, 7, 14, 2, 2, 7, 15, 8, 5, 15, 3, 5, 5, 5, 16, 6, 8, 17, 3, 2, 9, 18, 9, 3, 6, 4, 19, 9, 6, 5, 6, 6, 10, 7, 5, 10, 5, 4, 20, 4, 21, 7, 10, 7, 5, 11, 21, 11, 4, 5, 11, 6, 11
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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If Andrica's conjecture is true sequence is >=1.
Since Andrica's conjecture is bounded below only by zero, a(n) is not bounded above.
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REFERENCES
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C. A. Pickover, The Math Book, Sterling, NY, 2009; see p. 482.
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LINKS
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Eric Weisstein's World of Mathematics, Andrica's conjecture
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FORMULA
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Conjecture : for n>=4, a(n)>=2. More generally for any m >=1, the set of k such that a(k)=m is finite. i.e. if n>=217, a(n)>=3, if n>=263 a(n)>=4, if n>=590 a(n)>=5, if n>=3385 a(n)>=6 ...
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EXAMPLE
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a(1)=round(1/(sqrt(3)-sqrt(2)))=3
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CROSSREFS
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Sequence in context: A152159 A090341 A088435 this_sequence A068448 A054081 A164585
Adjacent sequences: A074973 A074974 A074975 this_sequence A074977 A074978 A074979
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KEYWORD
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nonn
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AUTHOR
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Werner Sand (werner.sand(AT)tiscalimail.de) and Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 06 2002
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