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

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

Author

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

Keywords

• nonn
• more

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