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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 A290711 A228837 Adjacent sequences:  A051498 A051499 A051500 * A051502 A051503 A051504 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 January 16 17:26 EST 2021. Contains 340206 sequences. (Running on oeis4.)