

A102470


Numbers n such that denominator of Sum_{k=0 to n} 1/k! is n!.


1



0, 1, 2, 4, 6, 8, 10, 16, 18, 20, 26, 28, 40, 46, 48, 58, 66, 68, 70, 80, 86, 96, 98, 118, 126, 130, 136, 146, 150, 170, 176, 178, 180, 188, 190, 206, 208, 210, 216, 230, 260, 266, 268, 278, 286, 288, 300, 306, 308, 326, 328, 338, 346, 358, 366, 370, 378, 380, 388
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OFFSET

1,3


COMMENTS

a(n) is even for n > 1, as Sum_{k=0 to n} 1/k! reduces to lower terms when n > 1 is odd.


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) = 2*A102471(n1) for n > 1.


EXAMPLE

1/0! + 1/1! + 1/2! + 1/3! +1/4! = 65/24 and 24 = 4!, so 4 is a member. But 1/0! + 1/1! + 1/2! + 1/3! = 8/3 and 3 < 3!, so 3 is not a member.


MATHEMATICA

fQ[n_] := (Denominator[Sum[1/k!, {k, 0, n}]] == n!); Select[ Range[0, 389], fQ[ # ] &] (* Robert G. Wilson v, Jan 15 2005 *)


CROSSREFS

For n > 0, n is a member <=> A093101(n) = 1 <=> A061355(n) = n! <=> A061355(n) = A002034(A061355(n))! <=> A061354(n) = 1+n+n(n1)+n(n1)(n2)+...+n!. See also A102471.
Sequence in context: A226809 A161562 A333019 * A057195 A088007 A302299
Adjacent sequences: A102467 A102468 A102469 * A102471 A102472 A102473


KEYWORD

nonn


AUTHOR

Jonathan Sondow, Jan 14 2005


EXTENSIONS

More terms from Robert G. Wilson v, Jan 15 2005


STATUS

approved



