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

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

Offset: 1

Author

Serge Batalov, Jul 14 2017

Keywords

• nonn
• hard
• more

Comments

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

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

Examples

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

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.

Crossrefs

Cf. A001272, A063833, A100614.

Programs

Mathematica

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 *)

PARI

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