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 A102582 Numbers n such that denominator of Sum_{k=0..4n+1} 1/k! is (4n+1)!/2. 2
 1, 3, 5, 15, 16, 21, 23, 28, 31, 35, 40, 41, 48, 60, 61, 68, 75, 80, 81, 85, 86, 88, 93, 96, 98, 100, 105, 111, 115, 118, 126, 131, 133, 138, 145, 146, 150, 151, 153, 156, 163, 178, 183, 190, 191, 200, 208, 211, 213, 226, 230, 243, 245, 248, 250, 256, 260, 261, 265 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The denominator of Sum_{k=0 to m} 1/k! is m!/d, where d = A093101(m). If m = 4n+1 > 1, then d is even. n is a member when d = 2. LINKS J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641. J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, arXiv:0704.1282 [math.HO], 2007-2010. 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) = A102581(n+1)/2. EXAMPLE 1/0! + 1/1! + 1/2! + 1/3! + 1/4! + 1/5! = 163/60 and 60 = 5!/2 = (4*1+1)!/2, so 1 is a member. MATHEMATICA fQ[n_] := (Denominator[ Sum[1/k!, {k, 0, 4n + 1}]] == (4n + 1)!/2); Select[ Range[0, 274], fQ[ # ] &] (* Robert G. Wilson v, Jan 24 2005 *) CROSSREFS n is a member <=> 2n is a member of A102581 <=> A093101(4n+1) = 2 <=> A061355(4n+1) = (4n+1)!/2. Sequence in context: A093015 A243940 A066420 * A089168 A103127 A103192 Adjacent sequences:  A102579 A102580 A102581 * A102583 A102584 A102585 KEYWORD nonn AUTHOR Jonathan Sondow, Jan 21 2005 EXTENSIONS More terms from Robert G. Wilson v, Jan 24 2005 STATUS approved

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Last modified July 24 18:34 EDT 2021. Contains 346273 sequences. (Running on oeis4.)