A245495 Primes of the form n! - (n+1)! + (n+2)! + 1.

103, 4441, 36650881, 5787936001, 19702293811201, 1075342687614074880001, 8547762518578406446202880000001, 59043709472234119545920159524322926688993280000000001, 698533028148544417308552639358841460358000936394290829866303488000000000001

Offset: 1

Author

K. D. Bajpai, Jul 24 2014

Keywords

• nonn

Comments

The next term a(10) has 95 digits which is too large to show in data section.

a(16) has 1181 digits, hence not included in b-file.

Primes for indices 3, 5, 9, 11, 14, 20, 27, 41, 54, 65, 81, 83, 105, 315, 323, 515, ... - Robert G. Wilson v, Aug 07 2014

Examples

			m = 3: m! - (m+1)! + (m+2)! + 1 = 103, which is prime, hence appears in the sequence.
m = 5: m! - (m+1)! + (m+2)! + 1 = 4441, which is prime, hence appears in the sequence.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..15

Crossrefs

Cf. A000040, A049984, A049432.

Programs

Mathematica

Select[Table[n! - (n + 1)! + (n + 2)! + 1, {n, 200}], PrimeQ[#] &]
Select[#[[1]]-#[[2]]+#[[3]]+1&/@Partition[Range[70]!,3,1],PrimeQ] (* Harvey P. Dale, Aug 20 2021 *)

PARI

a(n) = p=n!-(n+1)!+(n+2)!+1;if(ispseudoprime(p),return(p))
n=1;while(n<100,if(a(n),print1(a(n),", "));n++) \\ Derek Orr, Jul 27 2014