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 A288451 Numbers n such that !n + 7 is prime. 0
 0, 3, 4, 5, 7, 10, 12, 20, 37, 52, 73, 149, 304, 540, 2135, 7112, 7436, 9357 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS At present the terms >= 2135 are only probable primes. Expected to be finite, similar to Živković (1999). LINKS M. Živković, The number of primes Sum_{i=1..n} (-1)^(n-i)*i! is finite, Math. Comp. 68 (1999), no. 225, 403-409. EXAMPLE 4 is a term, because 0! + 1! + 2! + 3! + 7 = 17 is prime. MATHEMATICA Do[ If[ PrimeQ[ Sum[ k!, {k, 0, n - 1} ] + 7 ], Print[ n ] ], {n, 1, 600} ] PROG (PARI) s=0; for(n=0, 600, if(ispseudoprime(s + 7), print1(n, ", ")); s+=n!) CROSSREFS Cf. A001272, A063833, A100614. Sequence in context: A288427 A030502 A201025 * A236384 A073957 A309916 Adjacent sequences:  A288448 A288449 A288450 * A288452 A288453 A288454 KEYWORD nonn,hard,more AUTHOR Serge Batalov, Jul 14 2017 STATUS approved

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Last modified December 9 08:20 EST 2019. Contains 329877 sequences. (Running on oeis4.)