cp's OEIS Frontend

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.

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A060449 Generalized Mills numbers: a(n) = floor(c^(b^n)) where c=4.4, b=1.179.

Original entry on oeis.org

5, 7, 11, 17, 29, 53, 109, 252, 679, 2184, 8650, 43828, 296913, 2832896, 40474353, 930818760, 37522518949, 2931502379404, 499688559138590, 213681340556825047, 270268120176240462240, 1227682581046707804164120
Offset: 1

Views

Author

Jason Earls, Apr 07 2001

Keywords

Comments

First seven terms are primes.

Links

Crossrefs

Cf. A051254, A108739, A051021, A060699, A191357.

Programs

  • Maple
    Digits := 100; A060449 := n->4.4^(1.179^n);
  • PARI
    { default(realprecision, 2000); for (n=1, 44, write("b060449.txt", n, " ", floor(4.4^(1.179^n))); ) } \\ Harry J. Smith, Jul 05 2009

Extensions

More terms from James Sellers, Apr 11 2001
Offset changed from 0 to 1 by Harry J. Smith, Jul 05 2009

A060699 a(n) = floor(A^(C^n)), where A = 2.084551112207285611..., C = 1.221.

Original entry on oeis.org

2, 2, 3, 5, 7, 11, 19, 37, 83, 223, 739, 3181, 18911, 166679, 2376391, 60953117, 3202432763, 403823050201
Offset: 1

Views

Author

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

Keywords

Comments

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.
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

Examples

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

References

  • Jens Kruse Andersen. Personal communication (Feb 2009). [Luis Rodriguez-Torres (ludovicusmagister(AT)yahoo.com), Feb 10 2009]
  • O. Ore, Theory of Numbers and Its History. McGraw Hill, 1948.

Links

Crossrefs

Cf. A051254, A108739, A051021, A060449, A191357.

Formula

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