A245528 Primes of the form n! - (n + 1)! + (n + 2)! - 1.

19, 101, 35999, 327599, 3306239, 81430271999, 24779106953279078399999, 10501089199335077511167999999, 1372369506422963989169318155460666934165503999999999, 117024364553755119629556890816711613171571359743999999999

Offset: 1

Author

K. D. Bajpai, Jul 25 2014

Keywords

• nonn
• easy
• less

Comments

The term a(11) has 129 digits which is too large to show in data section.

a(15) has 1081 digits, hence not included in b-file.

The first 20 primes are for n = 2, 3, 6, 7, 8, 12, 21, 25, 40, 43, 83, 107, 132, 139, 478, 505, 931, 1516, 1739, 5208. - Jens Kruse Andersen, Aug 10 2014

Examples

			m = 2: m! - (m + 1)! + (m + 2)! - 1 = 19 which is prime, hence appears in the sequence.
m = 6: m! - (m + 1)! + (m + 2)! - 1 = 35999 which is prime, hence appears in the sequence.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..14

Crossrefs

Cf. A000040, A049984, A049432.

Programs

Magma

[a: n in [0..100] | IsPrime(a) where a is Factorial(n) - Factorial(n + 1) + Factorial(n + 2) - 1 ]; // Vincenzo Librandi, Aug 11 2014

Mathematica

Select[Table[n! - (n + 1)! + (n + 2)! - 1, {n, 200}], PrimeQ[#] &]

PARI

for(n=1,200,s=n!-(n+1)!+(n+2)!-1;if(ispseudoprime(s),print1(s,", "))) \\ Derek Orr, Aug 10 2014