A101746 Primes of the form ((0!)^2+(1!)^2+(2!)^2+...+(n!)^2)/6.

7, 103, 2503, 88903, 4322503, 2473107965928318342544472044975303

Offset: 1

Author

T. D. Noe, Dec 18 2004

Keywords

• fini
• nonn

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.

The next term (a(7)) has 96 digits. The largest term (a(9)) has 288 digits. - Harvey P. Dale, Aug 31 2021

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..9

Crossrefs

Cf. A061062 (S(n)), A100288 (primes of the form S(n)-1), A100289 (n such that S(n)-1 is prime), A101747 (n such that S(n)/6 is prime).

Programs

Mathematica

f2=1; s=2; Do[f2=f2*n*n; s=s+f2; If[PrimeQ[s/6], Print[{n, s/6}]], {n, 2, 100}]
Select[Accumulate[(Range[0,25]!)^2]/6,PrimeQ] (* Harvey P. Dale, Aug 31 2021 *)