OFFSET
0,1
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..4096
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, arXiv:0709.0671 [math.NT], 2007-2009; 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
EXAMPLE
a(5) = 4 because (5+3)/gcd(d(5),d(7)) = 8/gcd(2,20) = 8/2 = 4.
MATHEMATICA
(A[n_] := If[n==0, 1, n*A[n-1]+1]; d[n_] := GCD[A[n], n! ]; Table[(n+3)/GCD[d[n], d[n+2]], {n, 0, 79}])
(* Second program, faster: *)
Table[(n + 3)/Apply[GCD, Map[GCD[#!, Floor[E*#!] - Boole[# == 0]] &, n + {0, 2}]], {n, 0, 78}] (* Michael De Vlieger, Jul 12 2017 *)
PROG
(PARI)
A000522(n) = sum(k=0, n, binomial(n, k)*k!); \\ This function from Joerg Arndt, Dec 14 2014
m1=m2=1; for(n=0, 4096, m=m1; m1=m2; m2 = A093101(n+2); m124781 = gcd(m, m2); write("b093101.txt", n, " ", m); write("b124781.txt", n, " ", m124781); write("b123901.txt", n, " ", (n+3)/m124781)); \\ Antti Karttunen, Jul 12 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Sondow, Oct 18 2006
STATUS
approved