A096986 -id:A096986 - cp's OEIS frontend

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

Farideh Firoozbakht, Jul 31 2004

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

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

Cf. A096986, A090704, A049433.

<< 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 *)

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

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

A108270 Numbers k such that k*k! + (smallest prime >= k) is prime.

Original entry on oeis.org

1, 4, 6, 8, 30, 40, 164, 176, 189, 218, 370, 597, 603, 1473, 2176, 2436, 2548, 2732, 4758, 5574

Offset: 1

Jorge Coveiro, Jul 24 2006

Note that Maple, PARI etc. have different notions of what "next prime" means!

Cf. A096986.

Select[Range[5600],PrimeQ[# (#!) +NextPrime[#-1]]&] (* Harvey P. Dale, Oct 07 2019 *)

for(x=1,1000,if(isprime(x*x!+nextprime(x)),print1(x,",")))

A096986 INTERSECT A018252. - R. J. Mathar, Aug 13 2007

a(11)-a(20) from Donovan Johnson, Dec 13 2008

cp's OEIS Frontend

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

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