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A096985
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Numbers k such that k*k! - NextPrime(k) is prime.
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1
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3, 5, 8, 10, 12, 13, 23, 26, 30, 33, 38, 114, 162, 219, 265, 268, 277, 344, 463, 651, 877, 1128, 2466, 2594, 4828, 6512
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OFFSET
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1,1
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COMMENTS
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For a(23), the corresponding value of k*k! - NextPrime(k) has more than 6239 digits.
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LINKS
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EXAMPLE
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3 is in the sequence because 3*3! - 5 = 13 is prime.
8 is in the sequence because 8*8! - 11 = 322549 is prime.
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MATHEMATICA
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<< NumberTheory`NumberTheoryFunctions`; v={}; Do[If[PrimeQ [n*n!-NextPrime[n]], v=Append[v, n]; Print[v]], {n, 2150}]
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 *)
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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