A101747 Numbers n such that ((0!)^2+(1!)^2+(2!)^2+...+(n!)^2)/6 is prime.

3, 4, 5, 6, 7, 19, 40, 56, 93

Offset

1,1

Comments

Let S(n) = Sum_{i=0,..n-1} (i!)^2. Note that 6 divides S(n) for n>1. For prime p=20879, p divides S(p-1). Hence p divides S(n) for all n >= p-1 and all prime values of S(n)/6 are for n < p-1. These n yield provable primes for n <= 93. No other n < 4000.

No other n < 8000. [T. D. Noe, Jul 31 2008]

Links

Table of n, a(n) for n=1..9.

Mathematica

f2=1; s=2; Do[f2=f2*n*n; s=s+f2; If[PrimeQ[s/6], Print[{n, s/6}]], {n, 2, 100}]

Crossrefs

Cf. A061062 (S(n)), A100288 (primes of the form S(n)-1), A100289 (n such that S(n)-1 is prime), A101746 (primes of the form S(n)/6).

Sequence in context: A072599 A095138 A026475 * A355703 A134338 A084919

Adjacent sequences: A101744 A101745 A101746 * A101748 A101749 A101750

Keyword

fini,nonn

Author

T. D. Noe, Dec 18 2004

Status

approved