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.

A086681 Number of primes < 8^n.

Original entry on oeis.org

0, 4, 18, 97, 564, 3512, 23000, 155611, 1077871, 7603553, 54400028, 393615806, 2874398515, 21151907950, 156661034233, 1166746786182, 8731188863470, 65612899915304, 494890204904784, 3745011184713964, 28423094496953330, 216289611853439384, 1649819700464785589
Offset: 0

Views

Author

Cino Hilliard, Jul 28 2003

Keywords

Links

Crossrefs

Cf. A000720, A185192.

Programs

Formula

a(n) = A185192(3n). - R. J. Mathar, Sep 15 2012

Extensions

More terms from Harvey P. Dale, Mar 13 2011
a(15)-a(16) from Vincenzo Librandi, Mar 26 2017
a(17)-a(22) from David Baugh, Oct 08 2020

A141602 Integer part of 2^n/log(2^n).

Original entry on oeis.org

2, 2, 3, 5, 9, 15, 26, 46, 82, 147, 268, 492, 909, 1688, 3151, 5909, 11123, 21010, 39809, 75638, 144073, 275050, 526182, 1008516, 1936352, 3723754, 7171675, 13831089, 26708310, 51636066, 99940774, 193635250, 375535031, 728979766, 1416303547
Offset: 1

Views

Author

Cino Hilliard, Aug 21 2008

Keywords

Comments

2^n/log(2^n) is an approximation to the number of primes < 2^n.

Links

Crossrefs

Cf. A000799, A007525, A050500, A185192.

Programs

  • Magma
    A141602:= func< n | Floor(2^n/(n*Log(2))) >;
[A141602(n): n in [1..40]]; // G. C. Greubel, Sep 21 2024
  • Mathematica
    Floor[2^#/Log[2^#]]&/@Range[40] (* Harvey P. Dale, Mar 11 2013 *)
  • PARI
    g(n) = for(x=1,n,y=floor(2^x/log(2^x));print1(y","))
  • PARI
    a(n) = 2^n\log(2^n); \\ Michel Marcus, Feb 24 2021
  • SageMath
    def A141602(n): return int(2^n/(n*log(2)))
[A141602(n) for n in range(1,41)] # G. C. Greubel, Sep 21 2024

Formula

a(n) = A050500(2^n) = floor(2^n*A007525/n) >= A000799(n). - R. J. Mathar, Jan 05 2009

A374403 Number of n-bit primes.

Original entry on oeis.org

0, 2, 2, 2, 5, 7, 13, 23, 43, 75, 137, 255, 464, 872, 1612, 3030, 5709, 10749, 20390, 38635, 73586, 140336, 268216, 513708, 985818, 1894120, 3645744, 7027290, 13561907, 26207278, 50697537, 98182656, 190335585, 369323305, 717267168, 1394192236, 2712103833, 5279763824
Offset: 1

Views

Author

Jon E. Schoenfield, Jul 07 2024

Keywords

Comments

Number of primes whose binary expansion is n digits long.
a(n) is the number of primes in the half-open interval [2^(n-1), 2^n).
First differences of A185192.
See A007053 for additional information.

Examples

			a(1) = 0 because neither 0 nor 1 is a prime.
a(2) = 2 because the 2-bit primes are 10_2 = 2 and 11_2 = 3.
a(4) = 2 because the 4-bit primes are 1011_2 = 11 and 1101_2 = 13.

Crossrefs

Essentially the same as A036378 and A162145.
Cf. A185192 (partial sums).
Cf. A000720, A007053.

Programs

  • Mathematica
    a[n_]:=Sum[Boole[PrimeQ[i]],{i,2^(n-1),2^n-1}]; Array[a,38] (* Stefano Spezia, Jul 07 2024 *)

Formula

a(n) = A162145(n) for n >= 2. - Amiram Eldar, Jul 08 2024
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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