

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
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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

Table of n, a(n) for n=1..59.
J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637641.
J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, arXiv:0704.1282 [math.HO], 20072010.
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.
Index entries for sequences related to factorial numbers


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



