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A288451
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Numbers n such that !n + 7 is prime.
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0
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0, 3, 4, 5, 7, 10, 12, 20, 37, 52, 73, 149, 304, 540, 2135, 7112, 7436, 9357
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OFFSET
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1,2
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COMMENTS
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At present the terms >= 2135 are only probable primes.
Expected to be finite, similar to Živković (1999).
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LINKS
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EXAMPLE
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4 is a term, because 0! + 1! + 2! + 3! + 7 = 17 is prime.
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MATHEMATICA
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Do[ If[ PrimeQ[ Sum[ k!, {k, 0, n - 1} ] + 7 ], Print[ n ] ], {n, 1, 600} ]
Join[{0}, Flatten[Position[Accumulate[Range[0, 600]!]+7, _?PrimeQ]]] (* The program generates the first 14 terms. To generate more increase the Range constant, but the program may take a long time to run. *) (* Harvey P. Dale, May 21 2021 *)
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PROG
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(PARI) s=0; for(n=0, 600, if(ispseudoprime(s + 7), print1(n, ", ")); s+=n!)
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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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STATUS
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approved
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