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Search: id:A084141
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| A084141 |
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a(n) is the index in sequence A084138 when the value of that sequence is one (1), i.e. there is exactly one case where there are exactly a(n) primes between m and 2m, exclusively, for m>0. |
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6
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| 0, 22, 36, 47, 79, 98, 114, 134, 173, 178, 184, 210, 218, 221, 245, 254, 262, 284, 297, 305, 327, 333, 373, 387, 396, 426, 459, 466, 470, 484, 530, 544, 563, 567, 575, 587, 616, 650, 694, 700, 706, 708, 737, 776, 859, 881, 885, 898, 926, 939, 974, 993, 1002
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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This calculation relies on the fact that Pi(2*m)-Pi(m) > m/(3*Log(m)) for m>=5. Conjecture: There are an infinite number of terms in this sequence (Harry J. Smith).
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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(3)=47 because the 3rd one in sequence A084138 is its item 47. There is
exactly one case where there are exactly 47 primes between m and 2m.
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CROSSREFS
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Cf. A060715, A060756, A084138, A084139, A084140, A084142.
Adjacent sequences: A084138 A084139 A084140 this_sequence A084142 A084143 A084144
Sequence in context: A124317 A100039 A061561 this_sequence A082261 A063252 A078540
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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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