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

7, 103, 2503, 88903, 4322503, 2473107965928318342544472044975303

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.

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

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 *)

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).

Sequence in context: A234292 A357347 A177752 * A318398 A318815 A195246

Adjacent sequences: A101743 A101744 A101745 * A101747 A101748 A101749

Keyword

fini,nonn

Author

T. D. Noe, Dec 18 2004

Status

approved