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A288451 Numbers n such that !n + 7 is prime. 0

%I

%S 0,3,4,5,7,10,12,20,37,52,73,149,304,540,2135,7112,7436,9357

%N Numbers n such that !n + 7 is prime.

%C At present the terms >= 2135 are only probable primes.

%C Expected to be finite, similar to Živković (1999).

%H M. Živković, <a href="https://doi.org/10.1090/S0025-5718-99-00990-4">The number of primes Sum_{i=1..n} (-1)^(n-i)*i! is finite</a>, Math. Comp. 68 (1999), no. 225, 403-409.

%e 4 is a term, because 0! + 1! + 2! + 3! + 7 = 17 is prime.

%t Do[ If[ PrimeQ[ Sum[ k!, {k, 0, n - 1} ] + 7 ], Print[ n ] ], {n, 1, 600} ]

%o (PARI) s=0; for(n=0,600,if(ispseudoprime(s + 7),print1(n,", ")); s+=n!)

%Y Cf. A001272, A063833, A100614.

%K nonn,hard,more

%O 1,2

%A _Serge Batalov_, Jul 14 2017

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Last modified January 24 13:52 EST 2020. Contains 331194 sequences. (Running on oeis4.)