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A060699
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a(n) = floor(A^(C^n)), where A = 2.084551112207285611..., C = 1.221.
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2
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2, 2, 3, 5, 7, 11, 19, 37, 83, 223, 739, 3181, 18911, 166679, 2376391, 60953117, 3202432763, 403823050201
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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]
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REFERENCES
| 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
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LINKS
| C. K. Caldwell, Mills' Theorem - a generalization
Carlos Rivera, Puzzle 85
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FORMULA
| a(n) = floor [A^(C^n)] ; A = 2.084551112... ; C = 1.221 [From Luis Rodriguez-Torres (ludovicusmagister(AT)yahoo.com), Feb 10 2009]
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EXAMPLE
| 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]
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CROSSREFS
| Cf. A060449.
Sequence in context: A196375 A147997 A118987 * A062724 A126024 A179316
Adjacent sequences: A060696 A060697 A060698 * A060700 A060701 A060702
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KEYWORD
| nonn
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AUTHOR
| Luis Rodriguez-Torres (ludovicusmagister(AT)yahoo.com), Apr 20 2001
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