|
Search: id:A084140
|
|
|
| A084140 |
|
Guaranteed number of primes between m and 2m. |
|
+0
5
|
|
| 2, 6, 9, 15, 21, 24, 30, 34, 36, 49, 51, 54, 64, 75, 76, 84, 90, 91, 114, 115, 117, 120, 121, 132, 135, 141, 154, 156, 174, 175, 184, 187, 201, 205, 210, 216, 217, 220, 231, 244, 246, 252, 285, 286, 294, 297, 300, 301, 304, 321, 322, 324, 327, 330, 339, 360, 364
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
For all m>=a(n) there are at least n primes between m and 2m exclusively. This calculation relies on the fact that Pi(2*m)-Pi(m) > m/(3*Log(m)) for m>=5. This is one more than the terms of A084139 with offset changed from 0 to 1.
|
|
REFERENCES
|
P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 140.
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. Bertrand's Postulate.
|
|
EXAMPLE
|
a(11)=51 since there are at least 11 primes between m and 2m for all m>=51 and
this is not true for any m<51. Although a(100)=720 is not listed, for all
m>=720, there are at least 100 primes between m and 2m.
|
|
CROSSREFS
|
Cf. A060715, A060756, A084138, A084139, A084141, A084142.
Sequence in context: A049634 A120387 A084265 this_sequence A103139 A049622 A043548
Adjacent sequences: A084137 A084138 A084139 this_sequence A084141 A084142 A084143
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 15 2003
|
|
|
Search completed in 0.002 seconds
|
