The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A061354 Numerator of Sum_{k=0..n} 1/k!. 21
 1, 2, 5, 8, 65, 163, 1957, 685, 109601, 98641, 9864101, 13563139, 260412269, 8463398743, 47395032961, 888656868019, 56874039553217, 7437374403113, 17403456103284421, 82666416490601, 6613313319248080001, 69439789852104840011 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS p divides a(p-1) for prime p = {2, 5, 13, 37, 463, ...} which apparently coincides with A064384(n) = {2, 5, 13, 37, 463, ...} Primes p such that p divides 0!-1!+2!-3!+...+(-1)^{p-1}(p-1)!. - Alexander Adamchuk, Jun 14 2007 GCD(a(n), a(n+2)) = A124779(n) is either 1 or a prime 2, 5, 13, 37, 463, ... = A064384. - Jonathan Sondow, Jun 12 2007 For proofs of Adamchuk's and my Comments, see the link "The Taylor series for e ...". - Jonathan Sondow, Jun 18 2007 LINKS Harry J. Smith, Table of n, a(n) for n = 0..200 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 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) = A000522(n)/A093101(n). Numerators of floor(n!*exp(1))/n!, n>=1. Numerators of coefficients in expansion of exp(x)/(1-x). - Vladeta Jovovic, Aug 11 2002 a(n) = (1+n+n(n-1)+...+n!)/GCD(n!,1+n+n(n-1)+...+n!). - Jonathan Sondow, Aug 18 2006 EXAMPLE 1, 2, 5/2, 8/3, 65/24, 163/60, 1957/720, 685/252, ... MATHEMATICA exp[n_]:=Apply[Plus, 1/Range[0, n]!]; Numerator[Table[exp[n], {n, 0, 21}]]  (* Geoffrey Critzer, May 05 2013 *) A061354[n_] := Numerator[Sum[1/k!, {k, 0, n}]]; Array[A061354, 22, 0] (* JungHwan Min, Nov 08 2016 *) Accumulate[1/Range[0, 30]!]//Numerator (* Harvey P. Dale, Apr 13 2018 *) PROG (PARI) { default(realprecision, 500); e=exp(1); for (n=0, 200, a=numerator(floor(n!*e)/n!); if (n==0, a=1); write("b061354.txt", n, " ", a) ) } \\ Harry J. Smith, Jul 21 2009 CROSSREFS Cf. A061355 (denominators), A093101, A064384, A064384, A124779, A129924. Sequence in context: A268660 A180627 A264860 * A162709 A242875 A222897 Adjacent sequences:  A061351 A061352 A061353 * A061355 A061356 A061357 KEYWORD nonn,frac AUTHOR Amarnath Murthy, Apr 28 2001 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 9 07:57 EDT 2021. Contains 343693 sequences. (Running on oeis4.)