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.

Showing 1-3 of 3 results.

A063636 a(n) = floor((1287/545)^n).

Original entry on oeis.org

2, 5, 13, 31, 73, 173, 409, 967, 2283, 5392, 12735, 30073, 71017, 167706, 396032, 935217, 2208486, 5215270, 12315692, 29083113, 68678837, 162182870, 382989640, 904417737, 2135753445, 5043513182, 11910094433, 28125305569, 66417005997
Offset: 1

Views

Author

Jud McCranie, Aug 10 2001

Keywords

Comments

The first eight terms are primes. Does there exist a number theta such that the floor of theta^n is always prime?

Examples

			(1287/545)^3 = 13.16879..., so a(3)=13.
		

References

  • Richard Crandall and Carl Pomerance, Prime Numbers - a Computational Perspective, Springer, 2001, page 69, exercise 1.75.

Crossrefs

Programs

  • PARI
    { for (n=1, 300, write("b063636.txt", n, " ", 1287^n \ 545^n); ) } \\ Harry J. Smith, Aug 26 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.

Crossrefs

Formula

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

A191357 Floor(A^(C^n)), where A = 32.76 and C = 1.33.

Original entry on oeis.org

103, 479, 3673, 55147, 2024063, 243937297, 142915724779, 685893080269745, 53978528420922581864, 175329092084368391071206608, 80227969100540338877503013472650510, 26469961649988241699181245714190498215773679043
Offset: 1

Views

Author

Arkadiusz Wesolowski, May 31 2011

Keywords

Comments

First seven terms are primes.

Examples

			a(2) = 479 because 32.76^(1.33^2) = 479.1724192479....
		

Crossrefs

Programs

  • PARI
    default(realprecision, 100); for(n=1, 12, print1(floor(32.76^(1.33^n)), ", ")); \\ Arkadiusz Wesolowski, Jul 18 2011

Formula

a(n) = floor(32.76^(1.33^n)).
Showing 1-3 of 3 results.