1,1

Results from the application of Caldwell's Generalized Mills' Theorem. This value of A produces 18 primes. For 20 primes A must be adjusted to 2.084551112207285611.

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 =.5*(log A)^2 = 0.269784 This value disminishes with n. Example: For n = 23. A change in Y(23) by 2630 only changes Y(22) by .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. [From Luis Rodriguez-Torres (ludovicusmagister(AT)yahoo.com), Feb 10 2009]

Jens Kruse Anderson. - Personal communication (Feb 2009) [From Luis Rodriguez-Torres (ludovicusmagister(AT)yahoo.com), Feb 10 2009]

O. Ore, Theory of Numbers and its History . Mc Graw Hill 1948

C. K. Caldwell, Mills' Theorem - a generalization

C. Rivera, Prime Puzzles

Luis Rodriguez A generalization of Mills Theorem [From Luis Rodriguez-Torres (ludovicusmagister(AT)yahoo.com), Feb 10 2009]

a(n) = floor [A^(C^n)] ; A = 2.084551112... ; C = 1.221 [From Luis Rodriguez-Torres (ludovicusmagister(AT)yahoo.com), Feb 10 2009]

a(10) = 223 because 2.0845511122073^(1.221^10)= 223.58376...

With the value of A received from Jens K. Anderson we have: For n = 23 a(23) = 313 990 383 602 932 052 632 553 770 22009 [From Luis Rodriguez-Torres (ludovicusmagister(AT)yahoo.com), Feb 10 2009]

Sequence in context: A125189 A147997 A118987 this_sequence A062724 A126024 A127678

Adjacent sequences: A060696 A060697 A060698 this_sequence A060700 A060701 A060702

nonn

Luis Rodriguez-Torres (ludovicusmagister(AT)yahoo.com), Apr 20 2001