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

%I #19 Sep 08 2022 08:46:08

%S 19,101,35999,327599,3306239,81430271999,24779106953279078399999,

%T 10501089199335077511167999999,

%U 1372369506422963989169318155460666934165503999999999,117024364553755119629556890816711613171571359743999999999

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

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

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

%C 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

%H K. D. Bajpai, <a href="/A245528/b245528.txt">Table of n, a(n) for n = 1..14</a>

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

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

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

%o (PARI)

%o for(n=1,200,s=n!-(n+1)!+(n+2)!-1;if(ispseudoprime(s),print1(s,", "))) \\ _Derek Orr_, Aug 10 2014

%o (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

%Y Cf. A000040, A049984, A049432.

%K nonn,easy,less

%O 1,1

%A _K. D. Bajpai_, Jul 25 2014