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Search: id:A084139
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| A084139 |
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a(n) is the largest number for which exactly n primes are bounded between a(n) and 2a(n) exclusively. |
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6
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| 1, 5, 8, 14, 20, 23, 29, 33, 35, 48, 50, 53, 63, 74, 75, 83, 89, 90, 113, 114, 116, 119, 120, 131, 134, 140, 153, 155, 173, 174, 183, 186, 200, 204, 209, 215, 216, 219, 230, 243, 245, 251, 284, 285, 293, 296, 299, 300, 303, 320, 321, 323, 326, 329, 338, 359, 363
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) is the index of last occurrence of n in A060715. This calculation relies on the fact that Pi(2*m)-Pi(m) > m/(3*Log(m)) for m>=5. It can be shown that every integer >= 0 occurs in A060715, so there is no problem in finding the last occurrence.
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REFERENCES
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P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 140.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. Bertrand's Postulate.
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EXAMPLE
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a(10)=50 since ten primes last arise between 50 and 100
(53,59,61,67,71,73,79,83,89,97).
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CROSSREFS
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Cf. A060715, A060756, A084138, A084140, A084141, A084142.
Sequence in context: A020736 A020757 A049693 this_sequence A092590 A065394 A124011
Adjacent sequences: A084136 A084137 A084138 this_sequence A084140 A084141 A084142
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KEYWORD
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nonn
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AUTHOR
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Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 15 2003
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