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 A051254 Mills primes. 14
 2, 11, 1361, 2521008887, 16022236204009818131831320183, 4113101149215104800030529537915953170486139623539759933135949994882770404074832568499 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Mills showed that there is a number A > 1 but not an integer, such that floor( A^(3^n) ) is a prime for all n = 1, 2, 3, ... A is approximately 1.306377883863... (see A051021). Obverse of this is A118910 a(1) = 2; a(n) is greatest prime < a(n-1)^3. - Jonathan Vos Post, May 05 2006 REFERENCES T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 8. LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..8 Chris K. Caldwell, Mills' Theorem - a generalization Chris K. Caldwell and Yuanyou Chen, Determining Mills' Constant and a Note on Honaker's Problem, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.1. S. R. Finch, Mills' Constant James Grime and Brady Haran, Awesome Prime Number Constant, Numberphile video, 2013. Brian Hayes, Pumping the Primes, bit-player, Aug 19 2015. W. H. Mills, A prime-representing function, Bull. Amer. Math. Soc., Vol. 53 (1947), p. 604. László Tóth, A Variation on Mills-Like Prime-Representing Functions, arXiv:1801.08014 [math.NT], 2018. Eric Weisstein's World of Mathematics, Mills' Prime Eric Weisstein's World of Mathematics, Prime Formulas Eric W. Weisstein, Table of n, a(n) for n = 1..13 FORMULA a(1) = 2; a(n) is least prime > a(n-1)^3. - Jonathan Vos Post, May 05 2006 EXAMPLE a(3) = 1361 = 11^3 + 30 = a(2)^3 + 30 and there is no smaller k such that a(2)^3 + k is prime. - Jonathan Vos Post, May 05 2006 a(4) = 16022236204009818131831320183 = a(3)^3 + 80 = 2521008887^3 + 80 and there is no smaller k such that a(3)^3 + k is prime. - Jonathan Vos Post, May 05 2006 MAPLE floor(A^(3^n), n=1..10); # A is Mills's constant: 1.306377883863080690468614492602605712916784585156713644368053759966434.. (A051021). MATHEMATICA p = 1; Table[p = NextPrime[p^3], {6}] (* T. D. Noe, Sep 24 2008 *) NestList[NextPrime[#^3] &, 2, 5] (* Harvey P. Dale, Feb 28 2012 *) PROG (PARI) a(n)=if(n==1, 2, nextprime(a(n-1)^3)) \\ Charles R Greathouse IV, Jun 23 2017 CROSSREFS Cf. A001358, A055496, A076656, A006992, A005384, A005385, A118908, A118909, A118910, A118911, A118912, A118913. Cf. A224845 (integer lengths of Mills primes). Cf. A108739 (sequence of offsets b_n associated with Mills primes). Cf. A051021 (decimal expansion of Mills constant). Sequence in context: A034388 A131316 A062636 * A095820 A101295 A131306 Adjacent sequences:  A051251 A051252 A051253 * A051255 A051256 A051257 KEYWORD nonn,nice AUTHOR EXTENSIONS Edited by N. J. A. Sloane, May 05 2007 STATUS approved

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Last modified September 25 15:25 EDT 2018. Contains 315392 sequences. (Running on oeis4.)