A096985 Numbers k such that k*k! - NextPrime(k) is prime.

3, 5, 8, 10, 12, 13, 23, 26, 30, 33, 38, 114, 162, 219, 265, 268, 277, 344, 463, 651, 877, 1128, 2466, 2594, 4828, 6512

Offset: 1

Author

Farideh Firoozbakht, Jul 31 2004

Keywords

• nonn
• hard
• more

Comments

For a(23), the corresponding value of k*k! - NextPrime(k) has more than 6239 digits.

Examples

			3 is in the sequence because 3*3! - 5 = 13 is prime.
8 is in the sequence because 8*8! - 11 = 322549 is prime.
		

Crossrefs

Cf. A096986, A090704, A049433.

Programs

Mathematica

<< NumberTheory`NumberTheoryFunctions`;v={};Do[If[PrimeQ [n*n!-NextPrime[n]], v=Append[v, n];Print[v]], {n, 2150}]
Select[Range[900],PrimeQ[# #!-NextPrime[#]]&] (* The program generates the first 21 terms of the sequence. To select more, increase the Range constant but the program may take a long time to run. *) (* Harvey P. Dale, Aug 16 2023 *)

Extensions

a(23)-a(24) from Ryan Propper, Jan 01 2008

a(25)-a(26) from Michael S. Branicky, Aug 21 2023