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.

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

A151893 a(n) = smallest number k such that n! + k-th prime after n! is prime.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 2, 4, 10, 2, 4, 3, 1, 1, 4, 2, 9, 14, 1, 6, 14, 6, 5, 1, 11, 3, 35, 14, 20, 4, 1, 10, 1, 1, 6, 37, 33, 25, 17, 62, 2, 5, 26, 12, 10, 11, 37, 9, 9, 4, 50, 32, 9, 9, 7, 9, 47, 10, 40, 80, 60, 3, 18, 6, 2, 1
Offset: 1

Views

Author

Artur Jasinski, Apr 12 2008

Keywords

Links

Crossrefs

Cf. A002981, A151892, A151894, A151903, A139213, A139214.

Programs

  • Mathematica
    a = {}; Do[k = 1; While[ ! PrimeQ[n! + NextPrime[n!, k]], k++ ]; Print[k]; AppendTo[a, k], {n, 1, 200}]; a

A151894 Numbers k such that k! + second prime after k! is prime.

Original entry on oeis.org

2, 3, 5, 6, 7, 8, 11, 17, 42, 66, 76, 93, 139, 157, 226, 290, 415, 522, 774, 794, 1947
Offset: 1

Views

Author

Artur Jasinski, Apr 12 2008

Keywords

Comments

Because numbers of the form (k! + prime) are divisible by all primes <= k that means that the first prime number can have the form k! + next prime after k! and no primes of the form k! + m for m > 1 and m < next prime after k!.

Crossrefs

Cf. A002981, A151892, A151893, A151903.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[n! + NextPrime[n!,2]], AppendTo[a, n]], {n, 200}]; a
  • PARI
    is(k) = {my(f = k!); isprime(f + nextprime(nextprime(f + 1) + 1));} \\ Amiram Eldar, Oct 23 2024

Extensions

a(15)-a(20) from Amiram Eldar, Oct 23 2024
a(21) from Michael S. Branicky, Oct 24 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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