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%I #22 Aug 20 2021 18:04:55
%S 103,4441,36650881,5787936001,19702293811201,1075342687614074880001,
%T 8547762518578406446202880000001,
%U 59043709472234119545920159524322926688993280000000001,698533028148544417308552639358841460358000936394290829866303488000000000001
%N Primes of the form n! - (n+1)! + (n+2)! + 1.
%C The next term a(10) has 95 digits which is too large to show in data section.
%C a(16) has 1181 digits, hence not included in b-file.
%C 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
%H K. D. Bajpai, <a href="/A245495/b245495.txt">Table of n, a(n) for n = 1..15</a>
%e m = 3: m! - (m+1)! + (m+2)! + 1 = 103, which is prime, hence appears in the sequence.
%e m = 5: m! - (m+1)! + (m+2)! + 1 = 4441, which is prime, hence appears in the sequence.
%t Select[Table[n! - (n + 1)! + (n + 2)! + 1, {n, 200}], PrimeQ[#] &]
%t Select[#[[1]]-#[[2]]+#[[3]]+1&/@Partition[Range[70]!,3,1],PrimeQ] (* _Harvey P. Dale_, Aug 20 2021 *)
%o (PARI)
%o a(n) = p=n!-(n+1)!+(n+2)!+1;if(ispseudoprime(p),return(p))
%o n=1;while(n<100,if(a(n),print1(a(n),", "));n++) \\ _Derek Orr_, Jul 27 2014
%Y Cf. A000040, A049984, A049432.
%K nonn
%O 1,1
%A _K. D. Bajpai_, Jul 24 2014
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