|
| |
|
|
A051501
|
|
Bertrand primes III: a(n+1) is the smallest prime > 2^a(n).
|
|
2
|
| |
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
The terms in the sequence are floor(2^b), floor(2^2^b), floor(2^2^2^b), ..., where b is approximately 1.2516475977905.
The existence of b is a consequence of Bertrand's postulate.
a(5) is much larger than the largest known prime, which is currently only 2^32582657-1. - T. D. Noe, Oct 18 2007
This sequence is of course not computed from b; rather b is more precisely computed by determining the next term in the sequence.
|
|
|
REFERENCES
|
E. M. Wright, "A prime-representing function", The American Mathematical Monthly 58:9 (1951), pp. 616-618.
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Exercise 4.19.
|
|
|
LINKS
|
Table of n, a(n) for n=1..4.
|
|
|
EXAMPLE
|
The smallest prime after 2^5 = 32 is 37, so a(5) = 37.
|
|
|
CROSSREFS
|
Cf. A006992 (Bertrand primes), A079614 (Bertrand's constant), A227770 (Bertrand primes II).
Sequence in context: A210482 A053609 A036780 * A221681 A290711 A228837
Adjacent sequences: A051498 A051499 A051500 * A051502 A051503 A051504
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Jud McCranie
|
|
|
EXTENSIONS
|
Although the exact value of the next term is not known, it has 41373247571 digits.
Next term is 2.8024843513561521356110...e41373247570, where the next digit is 3 or 4. Under the Riemann hypothesis, the first 20686623775 digits are known. [From Charles R Greathouse IV, Oct 27 2010]
Edited by Franklin T. Adams-Watters, Aug 10 2009
Reference and bounds on next term from Charles R Greathouse IV, Oct 27 2010
Name clarified by Jonathan Sondow, Aug 02 2013
|
|
|
STATUS
|
approved
|
| |
|
|
