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A051501 Bertrand primes III: a(n+1) is the smallest prime > 2^a(n). 2
2, 5, 37, 137438953481 (list; graph; refs; listen; history; text; internal format)
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.
Robert Ballie comments that the next term is known to be 2.80248435135615213561103452115581... * 10^41373247570 via Dusart 2016, improving on my 2010 result in the Extensions section. - Charles R Greathouse IV, Aug 11 2020
REFERENCES
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Exercise 4.19.
LINKS
Pierre Dusart, Explicit estimates of some functions over primes, Ramanujan J. Vol 45 (2016), pp. 227-251.
E. M. Wright, A prime-representing function, Amer. Math. Monthly, 58 (1951), 616-618.
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 A347070 A290711
KEYWORD
nonn
AUTHOR
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

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)