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Search: id:A084142
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| A084142 |
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There are a unique number of primes between a(n) and 2a(n). This is a list of all such integers > zero in numerical order. |
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5
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| 1, 120, 216, 300, 531, 714, 804, 999, 1344, 1356, 1395, 1680, 1764, 1770, 1959, 2046, 2121, 2325, 2484, 2511, 2760, 2826, 3150, 3285, 3396, 3744, 4044, 4116, 4146, 4314, 4710, 4839, 5046, 5070, 5136, 5250, 5586, 5970, 6411, 6459, 6501, 6504, 6846, 7275
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The number of primes between a(n) and 2a(n) is unique because no other number m has the same of primes between m and 2m, exclusively, for m>0. a(n) is the value of A060756 or A084139 when A084138 is one. Question: Is this sequence infinitely long?
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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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The number 120 is in the list because there are 22 primes between 120 and 240
and no other number m has 22 primes between m and 2m, m>0.
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CROSSREFS
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Cf. A060715, A060756, A084138, A084139, A084140, A084141.
Sequence in context: A069674 A003015 A098565 this_sequence A146950 A028976 A158130
Adjacent sequences: A084139 A084140 A084141 this_sequence A084143 A084144 A084145
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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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