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A051501
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Bertrand primes: a(n+1) is the smallest prime > 2^a(n).
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2
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OFFSET
| 1,1
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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 (noe(AT)sspectra.com), 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.
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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.
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EXAMPLE
| The smallest prime after 2^5 = 32 is 37, so a(5) = 37.
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CROSSREFS
| Cf. A079614 (Bertrand's constant).
Sequence in context: A084436 A053609 A036780 * A206155 A135378 A077398
Adjacent sequences: A051498 A051499 A051500 * A051502 A051503 A051504
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KEYWORD
| nonn
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AUTHOR
| Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu)
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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 2 or 3. Under the Riemann hypothesis, the first 20686623775 digits are known. [From Charles R Greathouse IV (charles.greathouse(AT)case.edu), Oct 27 2010]
Edited by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Aug 10 2009
Reference and bounds on next term from Charles R Greathouse IV (charles.greathouse(AT)case.edu), Oct 27 2010
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