|
| |
| |
| |
|
|
|
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 (jvospost3(AT)gmail.com), May 05 2006
|
|
|
REFERENCES
| T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 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 prime-representing function, Bull. Amer. Math. Soc., Vol. 53 (1947), p. 604.
|
|
|
LINKS
| 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, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
|
|
|
FORMULA
| a(1) = 2; a(n) is least prime > a(n-1)^3. - Jonathan Vos Post (jvospost3(AT)gmail.com), 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 (jvospost3(AT)gmail.com), 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 (jvospost3(AT)gmail.com), 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}] (* From T. D. Noe, Sep 24 2008 *)
|
|
|
CROSSREFS
| Cf. A001358, A055496, A076656, A006992, A005384, A005385, A118908-A118913.
Cf. A051021, A108739.
Sequence in context: A034388 A131316 A062636 * A095820 A101295 A131306
Adjacent sequences: A051251 A051252 A051253 * A051255 A051256 A051257
|
|
|
KEYWORD
| nonn,nice
|
|
|
AUTHOR
| Simon Plouffe (simon.plouffe(AT)gmail.com).
|
|
|
EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), May 05 2007
|
| |
|
|
