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.

User: Brian Kell

Brian Kell's wiki page.

Brian Kell has authored 4 sequences.

A253316 Number of 2n X 2n Takuzu grids.

Original entry on oeis.org

1, 2, 72, 4140, 4111116, 48183195384
Offset: 0

Author

Brian Kell, Dec 30 2014

Keywords

Comments

A Takuzu grid is a 2n X 2n zero-one matrix with the following properties:
1. Every row and every column has n zeros and n ones.
2. No row or column has three consecutive zeros or three consecutive ones.
3. All rows are distinct, and all columns are distinct (but a row may be the same as a column).

Examples

			The following is a 4 X 4 Takuzu grid:
[ 0  1  1  0 ]
[ 1  0  0  1 ]
[ 0  0  1  1 ]
[ 1  1  0  0 ]
		

Crossrefs

Cf. A058527.
Number of possible rows equals A003440.

Extensions

a(5) from Frans J. Faase, Dec 14 2015

A145835 Number of compositions of the n X n grid graph.

Original entry on oeis.org

1, 12, 1434, 1691690, 19719299768, 2271230282824746, 2584855762327078145444, 29068227444022728740767607050, 3230042572278849047360048508956727420, 3546545075986984198328715750838554116235343894
Offset: 1

Author

Brian Kell, Oct 21 2008

Keywords

Comments

The number of compositions of the n X n grid graph is the number of partitions of an n X n square into regions of orthogonally connected unit squares.

Examples

			For n=2 the a(2)=12 partitions of a 2x2 square are: 1 partition into a single 2x2 region; 4 partitions into a 3-square 'L' shape and an isolated corner; 2 partitions into 2 1x2 bricks; 4 partitions into a 1x2 brick and 2 isolated squares; and 1 partition into 4 isolated squares.
		

Crossrefs

Cf. A110476.

Extensions

Terms for n=7,8,9 from Frank Simon, Oct 25 2011
a(10) from Frank Simon's thesis added by N. J. A. Sloane, Jan 04 2013

A099350 Numbers k such that 4*k! - 1 is prime.

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 10, 11, 51, 63, 197, 313, 579, 1264, 2276, 2669, 4316, 4382, 4678, 7907, 10843
Offset: 1

Author

Brian Kell, Oct 12 2004

Keywords

Comments

a(19) > 4570. - Jinyuan Wang, Feb 04 2020

Examples

			k = 5 is here because 4*5! - 1 = 479 is prime.
		

Programs

  • Maple
    for n from 0 to 1000 do if isprime(4*n! - 1) then print(n) end if end do;
  • Mathematica
    For[n = 0, True, n++, If[PrimeQ[4 n! - 1], Print[n]]] (* Jean-François Alcover, Sep 23 2015 *)
  • PARI
    is_A099350(n)=ispseudoprime(n!*4-1) \\ M. F. Hasler, Sep 20 2015

Extensions

a(14) from Alois P. Heinz, Sep 21 2015
a(15)-a(16) from Jean-François Alcover, Sep 23 2015
a(17)-a(18) from Jinyuan Wang, Feb 04 2020
a(19) from Michael S. Branicky, May 16 2023
a(20)-a(21) from Michael S. Branicky, Jul 11 2024

A099351 Numbers k such that 5*k! - 1 is prime.

Original entry on oeis.org

3, 5, 8, 13, 20, 25, 51, 97, 101, 241, 266, 521, 1279, 1750, 2204, 2473, 4193, 5181, 10080
Offset: 1

Author

Brian Kell, Oct 12 2004

Keywords

Comments

a(15) > 1879. - Jinyuan Wang, Feb 04 2020
a(17) > 3500. - Michael S. Branicky, Mar 06 2021

Examples

			k = 5 is here because 5*5! - 1 = 599 is prime.
		

Programs

  • Maple
    for n from 0 to 1000 do if isprime(5*n! - 1) then print(n) end if end do;
  • Mathematica
    Select[Range[550],PrimeQ[5#!-1]&] (* Harvey P. Dale, Nov 27 2013 *)
  • PARI
    is(n)=ispseudoprime(5*n!-1) \\ Charles R Greathouse IV, Jun 13 2017
    
  • Python
    from sympy import isprime
    from math import factorial
    print([k for k in range(300) if isprime(5*factorial(k) - 1)]) # Michael S. Branicky, Mar 05 2021

Extensions

a(13)-a(14) from Jinyuan Wang, Feb 04 2020
a(15)-a(16) from Michael S. Branicky, Mar 05 2021
a(17)-a(18) from Michael S. Branicky, Apr 03 2023
a(19) from Michael S. Branicky, Jul 12 2024