




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(n1)^3.  Jonathan Vos Post, May 05 2006


REFERENCES

T. M. Apostol, Introduction to Analytic Number Theory, SpringerVerlag, 1976, page 8.
Chris K. Caldwell and Yuanyou Cheng, Determining Mills' Constant and a Note on Honaker's Problem, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.1.
W. H. Mills, A primerepresenting function, Bull. Amer. Math. Soc., Vol. 53 (1947), p. 604.


LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..8
C. K. Caldwell, Mills' Theorem  a generalization
C. 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
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(n1)^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 *)


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

Simon Plouffe.


EXTENSIONS

Edited by N. J. A. Sloane, May 05 2007


STATUS

approved



