

A101747


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


1




OFFSET

1,1


COMMENTS

Let S(n)=sum_{i=0,..n1} (i!)^2. Note that 6 divides S(n) for n>1. For prime p=20879, p divides S(p1). Hence p divides S(n) for all n >= p1 and all prime values of S(n)/6 are for n < p1. These n yield provable primes for n <= 93. No other n < 4000.
No other n < 8000. [From 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 * A134338 A084919 A153100
Adjacent sequences: A101744 A101745 A101746 * A101748 A101749 A101750


KEYWORD

fini,nonn


AUTHOR

T. D. Noe, Dec 18 2004


STATUS

approved



