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

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

Offset

1,1

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.

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A001272, A005165.

Sequence in context: A321875 A359808 A005165 * A280067 A158615 A321652

Adjacent sequences: A071825 A071826 A071827 * A071829 A071830 A071831

Keyword

nonn,fini

Author

Benoit Cloitre, Jun 08 2002

Extensions

Edited by R. J. Mathar, Aug 28 2007

Status

approved