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.

A091295 (Number of primes == 3 mod 4 less than 10^n) - (number of primes == 1 mod 4 less than 10^n).

Original entry on oeis.org

1, 2, 7, 10, 25, 147, 218, 446, 551, 5960, 14252, 63337, 118472, 183457, 951700, 3458334, 6284060, 2581691, 80743228, 259753425
Offset: 1

Views

Author

Enoch Haga, Feb 23 2004

Keywords

Examples

			a(1) = 1 because below 10^1 3 and 7 are 3 mod 4 and 5 is 1 mod 4 and the difference is 2-1=1.

References

  • Hans Riesel, Prime Numbers and Computer Methods for Factorization, 2nd ed., Birkhauser, The distribution of primes between the two series 4n+1 and 4n+3, pages 73-77, with graphs.

Links

Crossrefs

Cf. A091098, A091099. A002144, A002145, A091318, A091267.

Formula

a(n) = A091099(n) - A091098(n) = A093153(n) + 1. [Max Alekseyev, May 17 2009]

Extensions

a(17)-a(20) from Marc Deleglise, Jun 28 2007

A093151 Number of odd composites 1 mod 4 less than 10^n.

Original entry on oeis.org

1, 13, 169, 1890, 20216, 210824, 2167819, 22119495, 224576508, 2272476724, 22940979719, 231196075659, 2326967290816, 23397529216327, 235077715264515, 2360380831212204, 23688221424314913, 237630022857420415, 2382971166402199310, 23889590198849417292
Offset: 1

Views

Author

Enoch Haga, Mar 24 2004

Keywords

Examples

			Below 10^2 there are 13 odd composites so a(2)=13

Crossrefs

Cf. A093152 A093153 A091295 A091098 A091099.

Formula

Count odd composites 1 mod 4 less than 10^n
For n>1, a(n) = 25*10^(n-2) - 1 - A091098(n). - Max Alekseyev, May 30 2007

Extensions

More terms from Max Alekseyev, May 30 2007
Extended by Max Alekseyev, Oct 13 2009

A093152 Number of odd composites below 10^n that are congruent to 3 modulo 4.

Original entry on oeis.org

0, 12, 163, 1881, 20192, 210678, 2167602, 22119050, 224575958, 2272470765, 22940965468, 231196012323, 2326967172345, 23397529032871, 235077714312816, 2360380827753871, 23688221418030854, 237630022854838725, 2382971166321456083, 23889590198589663868
Offset: 1

Views

Author

Enoch Haga, Mar 24 2004

Keywords

Examples

			Below 10^2 there are 12 odd composites 3 mod 4 so a(2)=12

Crossrefs

Cf. A093151 A093153 A091295 A091098 A091099.

Formula

For n>1, a(n) = 25*10^(n-2) - A091099(n) [From Max Alekseyev, May 17 2009]

Extensions

a(9) from Ryan Propper, Jun 21 2005
a(10)-a(20) from Max Alekseyev, May 17 2009, Oct 08 2013
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.