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 1-5 of 5 results.

A066726 Numbers n such that binomial(2n, n) - 1 is prime.

Original entry on oeis.org

2, 3, 5, 9, 15, 29, 43, 51, 113, 184, 213, 222, 267, 279, 369, 402, 441, 603, 812, 839, 902, 1422, 1542, 1824, 2983, 3065, 3911, 3958, 4192, 4587, 4865, 5543, 5837, 7902, 9299, 9722, 10412, 10648, 11498, 12803, 14428, 15876, 20173, 26311, 38927, 52210, 54189, 59757, 60454, 72094, 76899, 85033, 91059, 91059
Offset: 1

Views

Author

Robert G. Wilson v, Jan 15 2002

Keywords

Comments

I.e., numbers n such that (2*n)!/(n!)^2-1 is prime. - Hugo Pfoertner, Sep 25 2005
The next term is > 30000. - Vaclav Kotesovec, May 03 2021
a(55) > 100000. - Robert Price, Jul 02 2024

Crossrefs

Cf. A066699, A085793.
Cf. A092751 = primes of the form (2*n)!/(n!)^2-1, A112853 = (2*n)!/n!-1 is prime, A112855 = (2*n)!/n!+1 is prime, A066699 = (2*n)!/(n!)^2+1 is prime, A112861 = (2*n)!/(2*(n!)^2)-1 is prime, A112863 = (2*n)!/(2*(n!)^2)+1 is prime. - Hugo Pfoertner, Sep 25 2005

Programs

  • Mathematica
    Do[ If[ PrimeQ[ Binomial[2n, n] - 1], Print[n]], {n, 1, 2000} ]
  • PARI
    is(n)=isprime(binomial(2*n,n)-1) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

More terms from Ed Pegg Jr, Sep 10 2003
Edited by N. J. A. Sloane, Aug 23 2008 at the suggestion of R. J. Mathar
a(43)-a(44) from Vaclav Kotesovec, May 03 2021
a(45)-a(54) from Robert Price, Jul 02 2024

A112861 Numbers k such that (2*k)!/(2*(k!)^2) - 1 is prime.

Original entry on oeis.org

2, 6, 10, 21, 45, 63, 306, 404, 437, 471, 646, 1174, 1192, 1334, 1975, 2397, 2410, 4305, 6111, 7852, 9488, 11120, 13304, 14408, 16075, 16238, 21188, 21659, 22025, 28673, 30793, 32178, 35278, 40049, 46516, 47836, 52157, 54531, 59897, 60275, 63362, 76139, 84219, 89024, 90783, 91605, 96761
Offset: 1

Views

Author

Hugo Pfoertner, Sep 30 2005

Keywords

Comments

a(48) > 100000. - Robert Price, Jul 25 2024

Crossrefs

Cf. A001700(n-1) = (2*n)!/(2*(n!)^2); A112862: primes of the form (2*n)!/(2*(n!)^2)-1; A112853: (2*n)!/n!-1 is prime; A112855: (2*n)!/n!+1 is prime; A066726: (2*n)!/(n!)^2-1 is prime; A066699: (2*n)!/(n!)^2+1 is prime; A112863: (2*n)!/(2*(n!)^2)+1 is prime.

Programs

  • Magma
    [n: n in [1..700] | IsPrime(Factorial(2*n) div (2*Factorial(n)^2)-1)]; // Vincenzo Librandi, Apr 10 2015
  • Mathematica
    Select[Range[10000], PrimeQ[(2 #)! / (2 (#!)^2) - 1 ] &] (* Vincenzo Librandi, Apr 10 2015 *)

Extensions

a(22)-a(26) from Vaclav Kotesovec, May 02 2021
a(27)-a(47) from Robert Price, Jul 25 2024

A112855 Numbers n such that (2*n)!/n!+1 is prime.

Original entry on oeis.org

1, 2, 5, 10, 24, 30, 72, 340, 379, 712, 1020, 1647, 3654, 7923
Offset: 1

Views

Author

Hugo Pfoertner, Sep 25 2005

Keywords

Comments

Next term is > 10000.

Crossrefs

Cf. A112856 primes of the form (2*n)!/n!+1, A112853 (2*n)!/n!-1 is prime, A066726 (2*n)!/(n!)^2-1 is prime, A112859 (2*n)!/(n!)^2+1 is prime, A112861 (2*n)!/(2*(n!)^2)-1 is prime, A112863 (2*n)!/(2*(n!)^2)+1 is prime.

Programs

  • Mathematica
    Select[Range[8000],PrimeQ[(2#)!/#!+1]&] (* Harvey P. Dale, Mar 23 2012 *)

A112863 Numbers k such that (2*k)!/(2*(k!)^2)+1 is prime.

Original entry on oeis.org

1, 3, 5, 6, 14, 19, 24, 45, 49, 62, 72, 122, 149, 197, 209, 222, 349, 409, 491, 527, 601, 675, 728, 769, 795, 853, 1039, 1318, 1599, 2069, 2279, 2567, 2634, 3286, 3482, 6880, 6919, 9117, 9276, 9564, 10898, 13061, 14570, 16493, 17366, 18773, 19901, 25569, 26611, 28322
Offset: 1

Views

Author

Hugo Pfoertner, Sep 30 2005

Keywords

Crossrefs

Cf. A001700, A112864, A112853, A112855, A066726, A112861.

Programs

  • Mathematica
    Select[Range[3000],PrimeQ[(2#)!/(2(#!)^2)+1]&] (* James C. McMahon, Jun 13 2024 *)
  • PARI
    isok(k) = ispseudoprime(1+binomial(2*k-1, k-1)); \\ Michel Marcus, Jun 14 2024

Extensions

a(42)-a(43) from Charles R Greathouse IV, Sep 26 2006
a(44)-a(50) from Michael S. Branicky, Jul 24 2024

A112854 Primes of the form (2*n)!/n!-1.

Original entry on oeis.org

11, 665279, 3497296636753919999, 1960781468160819415703172080467967999999
Offset: 1

Views

Author

Hugo Pfoertner, Sep 25 2005

Keywords

Comments

Next term (2*114)!/114!-1 has 254 decimal digits.

Crossrefs

A112853 gives n such that (2*n)!/n!-1 is prime, A112856 gives primes of the form (2*n)!/n!+1.
Showing 1-5 of 5 results.

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

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