A102471 Numbers n such that the denominator of Sum_{k=0 to 2n} 1/k! is (2n)!.

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

Offset

1,3

Comments

n is a member <=> A093101(2n) = 1 <=> A061355(2n) = (2n)! <=> A061355(2n) = A002034(A061355(2n))!.

Links

Table of n, a(n) for n=1..62.

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.

Index entries for sequences related to factorial numbers

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