

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
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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) 637641.


LINKS

Table of n, a(n) for n=1..62.
Index entries for sequences related to factorial numbers.
J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality
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



