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.

A084749 Numbers m such that m! + p is a prime, where p is the smallest prime > m.

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, 4884, 6822, 8070, 11079, 13659, 17659
Offset: 1

Views

Author

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

Keywords

Comments

Next term, if it exists, is >4800. - Ryan Propper, Jan 02 2007
From Farideh Firoozbakht, Oct 21 2009: (Start)
Numbers corresponding to a(19)-a(24) are probable primes.
There is no further term up to 8300. (End)

Examples

			727 = 6! + 7 is a prime but 8! + 11 is composite hence 6 is a member but 8 is not.
7 is in the sequence because 7!=5040, nextprime(7)=11 and 5040+11 is prime.

Crossrefs

Cf. A084748, A084750, A092028, A064278, A002981, A151892.

Programs

  • Mathematica
    Do[If[PrimeQ[k!+NextPrime[k]], Print[k]], {k, 0, 1525}] (* Farideh Firoozbakht, Feb 26 2004 *)
Select[Range[0,500],PrimeQ[#!+NextPrime[#]]&] (* The program generates the first 19 terms of the sequence. *) (* Harvey P. Dale, Jul 16 2025 *)

Extensions

More terms from Farideh Firoozbakht, Feb 26 2004
Edited by N. J. A. Sloane at the suggestion of Artur Jasinski, Apr 14 2008
a(22)-a(24) from Farideh Firoozbakht, Oct 21 2009
a(25) from Michael S. Branicky, Aug 05 2024
a(26)-a(27) from Michael S. Branicky, May 25 2025

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

A151903 a(n) = smallest number k such that n! + k-th prime after n is prime.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 5, 3, 1, 2, 5, 13, 2, 8, 3, 4, 5, 16, 2, 3, 3, 16, 23, 4, 8, 6, 10, 38, 18, 20, 11, 1, 14, 7, 21, 52, 2, 13, 4, 5, 12, 6, 1, 38, 12, 36, 1, 8, 3, 43, 1, 4, 32, 4, 19, 12, 45, 45, 41, 118, 14, 40, 1, 26, 43, 2, 4, 13, 15, 128, 6, 1, 20, 29, 9, 14, 9, 36, 6, 104, 9, 14, 26, 9
Offset: 1

Views

Author

Artur Jasinski, Apr 12 2008

Keywords

Comments

Because numbers of the form : (n! + prime) are divisible by all primes <= n that mean that first prime number can have form n! + k-th prime after n and no primes of the form n! + k for k > 1 and k < next prime after n

Links

Crossrefs

Cf. A002981, A151892, A151894, A151893, A139213, A139214.

Programs

  • Mathematica
    a = {}; Do[k = 1; While[ ! PrimeQ[n! + NextPrime[n, k]], 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 1-4 of 4 results.

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