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A051501
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Bertrand primes III: a(n+1) is the smallest prime > 2^a(n).
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2
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OFFSET
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1,1
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COMMENTS
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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
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REFERENCES
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R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Exercise 4.19.
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LINKS
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Table of n, a(n) for n=1..4.
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.
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EXAMPLE
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The smallest prime after 2^5 = 32 is 37, so a(5) = 37.
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CROSSREFS
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Cf. A006992 (Bertrand primes), A079614 (Bertrand's constant), A227770 (Bertrand primes II).
Sequence in context: A210482 A053609 A036780 * A221681 A347070 A290711
Adjacent sequences: A051498 A051499 A051500 * A051502 A051503 A051504
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KEYWORD
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nonn
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AUTHOR
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Jud McCranie
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EXTENSIONS
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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
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STATUS
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approved
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