Search: id:A101746
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%I A101746
%S A101746 7,103,2503,88903,4322503,2473107965928318342544472044975303
%N A101746 Primes of the form ((0!)^2+(1!)^2+(2!)^2+...+(n!)^2)/6.
%C A101746 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.
%t A101746 f2=1; s=2; Do[f2=f2*n*n; s=s+f2; If[PrimeQ[s/6], Print[{n, s/6}]], {n, 
               2, 100}]
%Y A101746 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).
%Y A101746 Sequence in context: A140633 A142400 A032460 this_sequence A001921 A098362 
               A093741
%Y A101746 Adjacent sequences: A101743 A101744 A101745 this_sequence A101747 A101748 
               A101749
%K A101746 fini,nonn
%O A101746 1,1
%A A101746 T. D. Noe (noe(AT)sspectra.com), Dec 18 2004

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