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A100289
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Numbers n such that (1!)^2 + (2!)^2 + (3!)^2 +...+ (n!)^2 is prime.
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4
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2, 3, 4, 5, 7, 8, 10, 18, 21, 42, 51, 91, 133, 177, 182, 310, 3175, 9566
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| All n <= 310 yield provable primes. No other n < 4000.
Write the sum as S(2,n)-1, where S(k,n) = sum_{i=0..n} (i!)^k. Let p=1248829. Because p divides S(2,p-1)-1, p divides S(2,n)-1 for all n >= p-1. Hence there are no primes for n >= p-1.
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LINKS
| Eric Weisstein's World of Mathematics, Integer Sequence Primes
Eric Weisstein's World of Mathematics, Factorial Sums
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MATHEMATICA
| Select[Range[1000], PrimeQ[Plus@@((Range[ # ]!)^2)]&]
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CROSSREFS
| Cf. A100288 (primes of the form (1!)^2 + (2!)^2 + (3!)^2 +...+ (k!)^2).
Cf. A061062 ((0!)^2 + (1!)^2 + (2!)^2 + (3!)^2 +...+ (n!)^2).
Sequence in context: A029003 A034296 A075745 * A054021 A066191 A166159
Adjacent sequences: A100286 A100287 A100288 * A100290 A100291 A100292
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KEYWORD
| nonn,fini
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Nov 11 2004 and Dec 11 2004
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EXTENSIONS
| More terms from T. D. Noe (noe(AT)sspectra.com), Feb 15 2006
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