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A124374
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Primes of the form !(k + 1)/2 = Sum_{i=0..k} i!/2.
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1
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2, 5, 17, 2957, 23117, 204557, 2018957, 4578979328975537786697650470157, 12572230784049013026617689884981971446439568309146114097251787122217783800812199225999909965168264460210470157
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OFFSET
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1,1
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COMMENTS
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Sum_{i=0..k} i! = k! + !k = A003422(k+1), where !k is left factorial !k = Sum_{i=0..k-1} i! = A003422(k). Left factorials are even for k > 1. Corresponding numbers k such that Sum_{i=0..k} i!/2 = A003422(k+1)/2 is prime are listed in A124375(n) = {2, 3, 4, 7, 8, 9, 10, 29, 75, 162, 270, 272, 353, ...}.
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LINKS
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FORMULA
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MATHEMATICA
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f=0; Do[f=f+n!; If[PrimeQ[f/2], Print[{n, f/2}]], {n, 0, 353}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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