A071828 Primes of the form Sum_{i=1..k} (-1)^(k-i)*i!.

5, 19, 101, 619, 4421, 35899, 3301819, 1226280710981, 115578717622022981, 32656499591185747972776747396512425885838364422981

Offset: 1

Author

Benoit Cloitre, Jun 08 2002

Keywords

• nonn
• fini

References

• R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section B43.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..14
• M. Zivkovic, The number of primes sum_(i=1..n)(-1)^(n-i)i! is finite, Math. Comp., vol. 68 (1999), pp. 403-409.

Crossrefs

Cf. A001272, A005165.

Programs

Mathematica

l = Abs@Accumulate[(-1)^#*#! & /@ Range@99]; l[[Flatten@Position[l, ?PrimeQ]]] (* _Hans Rudolf Widmer, Feb 27 2023 *)

PARI

for(n=1,120,if(isprime(abs(sum(i=1,n,(-1)^i*i!)))==1,print1(abs(sum(i=1,n,(-1)^i*i!)),",")))

PARI

v=[];for(n=1,1000, if(ispseudoprime(t=abs(sum(i=1,n,(-1)^i*i!))), v=concat(v,t))); v \\ Charles R Greathouse IV, Feb 14 2011

Formula

a(n) = A005165(A001272(n)).

Extensions

Edited by R. J. Mathar, Aug 28 2007