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%I #24 Aug 23 2023 08:37:14
%S 3,5,8,10,12,13,23,26,30,33,38,114,162,219,265,268,277,344,463,651,
%T 877,1128,2466,2594,4828,6512
%N Numbers k such that k*k! - NextPrime(k) is prime.
%C For a(23), the corresponding value of k*k! - NextPrime(k) has more than 6239 digits.
%e 3 is in the sequence because 3*3! - 5 = 13 is prime.
%e 8 is in the sequence because 8*8! - 11 = 322549 is prime.
%t << NumberTheory`NumberTheoryFunctions`;v={};Do[If[PrimeQ [n*n!-NextPrime[n]], v=Append[v, n];Print[v]], {n, 2150}]
%t 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 *)
%Y Cf. A096986, A090704, A049433.
%K nonn,hard,more
%O 1,1
%A _Farideh Firoozbakht_, Jul 31 2004
%E a(23)-a(24) from _Ryan Propper_, Jan 01 2008
%E a(25)-a(26) from _Michael S. Branicky_, Aug 21 2023