This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A060699 #13 Feb 22 2020 22:35:32 %S A060699 2,2,3,5,7,11,19,37,83,223,739,3181,18911,166679,2376391,60953117, %T A060699 3202432763,403823050201 %N A060699 a(n) = floor(A^(C^n)), where A = 2.084551112207285611..., C = 1.221. %C A060699 Results from the application of Caldwell's Generalized Mills's Theorem. This value of A produces 18 primes. For 20 primes A must be adjusted to 2.084551112207285611. %C A060699 The extension of the sequence is guaranteed by the Cramer conjecture. That is: If the needed change in Y(n) for obtaining the next prime (superior or inferior) is as maximum = (log Y(n))^2/2, then the effect on Y(n-1) is less than K*C^(2n-1)*Y(n-1)/Y(n). K = (1/2)*(log A)^2 = 0.269784 This value diminishes with n. Example: For n = 23, a change in Y(23) by 2630 only changes Y(22) by 0.0043. _Jens Kruse Anderson_ with A = 2.084551112197624209091521123 calculated Y(n) = floor(A^(C^n)) from n = 1 to n = 3, obtaining 22 different primes. - Luis Rodriguez-Torres (ludovicusmagister(AT)yahoo.com), Feb 10 2009 %D A060699 Jens Kruse Andersen. Personal communication (Feb 2009). [Luis Rodriguez-Torres (ludovicusmagister(AT)yahoo.com), Feb 10 2009] %D A060699 O. Ore, Theory of Numbers and Its History. McGraw Hill, 1948. %H A060699 C. K. Caldwell, <a href="http://www.utm.edu/research/primes/notes/proofs/A3n.html">Mills' Theorem - a generalization</a> %H A060699 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_085.htm">Puzzle 85</a> %F A060699 a(n) = floor(A^(C^n)); A = 2.084551112... ; C = 1.221. - Luis Rodriguez-Torres (ludovicusmagister(AT)yahoo.com), Feb 10 2009 %e A060699 a(10) = 223 because 2.0845511122073^(1.221^10)= 223.58376... %e A060699 With the value of A received from Jens K. Andersen we have: For n = 23, a(23) = 313 990 383 602 932 052 632 553 770 22009. - Luis Rodriguez-Torres (ludovicusmagister(AT)yahoo.com), Feb 10 2009 %Y A060699 Cf. A051254, A108739, A051021, A060449, A191357. %K A060699 nonn %O A060699 1,1 %A A060699 Luis Rodriguez-Torres (ludovicusmagister(AT)yahoo.com), Apr 20 2001