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 1-4 of 4 results.

A092026 Duplicate of A084749.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 10, 33, 44, 48, 52, 64, 73, 92, 119, 182, 487, 603, 987
Offset: 1

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Author

Keywords

A151892 Numbers m such that m! + (next prime after m!) is prime.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 14, 15, 20, 25, 32, 34, 35, 67, 89, 191, 316, 411, 1213, 1280, 2022, 2267
Offset: 1

Views

Author

Artur Jasinski, Apr 12 2008

Keywords

Crossrefs

Cf. A002981, A151894, A151893, A151903, A084749.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[n! + NextPrime[n! ]], AppendTo[a, n]], {n, 200}]; a (* Artur Jasinski *)
Select[Range[420],PrimeQ[#!+NextPrime[#!]]&] (* Harvey P. Dale, Aug 20 2021 *)

Extensions

a(17)-a(18) from Robert G. Wilson v, Jun 11 2010
a(19)-a(20) from Michael S. Branicky, May 27 2023
a(21)-a(22) from Michael S. Branicky, Aug 03 2024

A084750 Numbers k such that k! - p is a prime, where p is the smallest prime > k.

Original entry on oeis.org

4, 5, 10, 11, 12, 14, 29, 53, 81, 90, 116, 236, 323, 346, 1172, 2957, 8400, 14906
Offset: 1

Views

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 16 2003

Keywords

Comments

Numbers k such that k! - NextPrime(k) is prime.
If k != 3, there does not exist a prime p and a number k such that k! - NextPrime(k) < p < k! - 1. - Farideh Firoozbakht, Feb 26 2004

Examples

			10 is in the sequence because 10! = 3628800, NextPrime(10) = 11 and 3628800 - 11 = 3628789 is prime.

Crossrefs

Cf. A084749, A050299, A002982, A064401, A084751.

Programs

  • Mathematica
    Do[If[PrimeQ[k!-NextPrime[k]], Print[k]], {k, 0, 1425}] (* Farideh Firoozbakht, Feb 26 2004 *)

Extensions

More terms from Farideh Firoozbakht, Feb 26 2004
a(16) from Ryan Propper, Jul 09 2005
Edited by N. J. A. Sloane at the suggestion of Ryan Propper, Jan 26 2008
a(17) from Michael S. Branicky, Jun 21 2023
a(18) from Michael S. Branicky, Apr 28 2025

A084748 Primes of the form n! + p where p is the smallest prime > n.

Original entry on oeis.org

3, 5, 11, 29, 127, 727, 5051, 3628811, 8683317618811886495518194401280000037, 2658271574788448768043625811014615890319638528000000047, 12413915592536072670862289047373375038521486354677760000000053
Offset: 1

Views

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 16 2003

Keywords

Comments

Let a term k! + p = prime(r) then prime(r) -prime(r-1) >=p-1.

Examples

			727 = 6! + 7 belongs to this sequence but 8! +11 is composite and is not a member.

Crossrefs

Cf. A084749.

Formula

a(n) = A084749(n)!+A007918(A084749(n)+1). - David Wasserman, Jan 04 2005

Extensions

More terms from David Wasserman, Jan 04 2005
Showing 1-4 of 4 results.

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

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