

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 2^325826571.  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. AddisonWesley, Exercise 4.19.


LINKS



EXAMPLE

The smallest prime after 2^5 = 32 is 37, so a(5) = 37.


CROSSREFS



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]


STATUS

approved



