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A084138
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a(n) is the number of times n is in sequence A060715, i.e. there are exactly a(n) cases where there are exactly n primes between m and 2m, exclusively, for m>0.
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4
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1, 3, 4, 4, 7, 3, 5, 6, 2, 9, 6, 2, 5, 10, 7, 8, 5, 3, 9, 10, 6, 4, 1, 8, 6, 5, 5, 9, 11, 10, 6, 6, 10, 8, 5, 6, 1, 3, 8, 9, 9, 5, 18, 16, 5, 7, 3, 1, 3, 12, 5, 3, 3, 3, 9, 8, 16, 7, 5, 8, 15, 10, 4, 2, 8, 7, 10, 13, 17, 5, 8, 7, 9, 10, 3, 5, 3, 6, 6, 1, 6, 8, 3, 3, 10, 15, 14, 16, 7, 10, 14, 5, 5, 3, 8
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| This calculation relies on the fact that Pi(2*m)-Pi(m) > m/(3*Log(m)) for m>=5. It can be shown that a(n) is never zero, i.e. every integer >= 0 is in sequence A060715.
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REFERENCES
| P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 140.
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. Bertrand's Postulate.
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EXAMPLE
| A(22)=1 because there are 22 primes between 120 and 240, namely prime number
p(31)=127 through p(52)=239 and in no other case is there exactly 22 primes
between m and 2m exclusively.
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CROSSREFS
| Cf. A060715, A060756, A084139, A084140, A084141, A084142.
Sequence in context: A178450 A019462 A078071 * A127141 A014406 A154426
Adjacent sequences: A084135 A084136 A084137 * A084139 A084140 A084141
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KEYWORD
| nonn
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AUTHOR
| Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 15 2003
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