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 A102471 Numbers n such that the denominator of Sum_{k=0 to 2n} 1/k! is (2n)!. 1
 0, 1, 2, 3, 4, 5, 8, 9, 10, 13, 14, 20, 23, 24, 29, 33, 34, 35, 40, 43, 48, 49, 59, 63, 65, 68, 73, 75, 85, 88, 89, 90, 94, 95, 103, 104, 105, 108, 115, 130, 133, 134, 139, 143, 144, 150, 153, 154, 163, 164, 169, 173, 179, 183, 185, 189, 190, 194, 195, 198, 199, 204 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS n is a member <=> A093101(2n) = 1 <=> A061355(2n) = (2n)! <=> A061355(2n) = A002034(A061355(2n))!. REFERENCES J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly, 113 (2006) 637-641. LINKS J. Sondow and K. Schalm, Which partial sums of the Taylor series for e are convergents to e? (and a link to the primes 2, 5, 13, 37, 463), II, Gems in Experimental Mathematics (T. Amdeberhan, L. A. Medina, and V. H. Moll, eds.), Contemporary Mathematics, vol. 517, Amer. Math. Soc., Providence, RI, 2010. FORMULA a(n) = A102470(n+1)/2 for n > 0. EXAMPLE Sum_{k=0 to 6} 1/k! = 1957/720 and 720 = 6! = (2*3)!, so 3 is a member. But Sum_{k=0 to 12} 1/k! = 260412269/95800320 and 95800320 < 12! = (2*6)!, so 6 is not a member. MATHEMATICA fQ[n_] := (Denominator[Sum[1/k!, {k, 0, 2n}]] == (2n)!); Select[ Range[0, 204], fQ[ # ] &] (* Robert G. Wilson v, Jan 15 2005 *) CROSSREFS Cf. A102470, A093101, A061355, A002034. Sequence in context: A270430 A318932 A259185 * A243490 A094566 A190018 Adjacent sequences:  A102468 A102469 A102470 * A102472 A102473 A102474 KEYWORD nonn AUTHOR Jonathan Sondow, Jan 14 2005 EXTENSIONS More terms from Robert G. Wilson v, Jan 15 2005 STATUS approved

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Last modified April 21 07:53 EDT 2019. Contains 322327 sequences. (Running on oeis4.)