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A101746 Primes of the form ((0!)^2+(1!)^2+(2!)^2+...+(n!)^2)/6. 1
7, 103, 2503, 88903, 4322503, 2473107965928318342544472044975303 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=1..6.

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), A101747 (n such that S(n)/6 is prime).

Sequence in context: A188946 A234292 A177752 * A318398 A318815 A195246

Adjacent sequences:  A101743 A101744 A101745 * A101747 A101748 A101749

KEYWORD

fini,nonn

AUTHOR

T. D. Noe, Dec 18 2004

STATUS

approved

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Last modified June 19 10:09 EDT 2021. Contains 345126 sequences. (Running on oeis4.)