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 A270587 Denominators of r-Egyptian fraction expansion for 1/e, where r(k) = 1/(k+1). 1
 2, 3, 37, 17282, 292943843, 105008217236608424, 15721030895760728441349083553863848, 293537352086847609928310098819595906620056713567902655641220410550838 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Suppose that r is a sequence of rational numbers r(k) <= 1 for k >= 1, and that x is an irrational number in (0,1).  Let f(0) = x, n(k) = floor(r(k)/f(k-1)), and f(k) = f(k-1) - r(k)/n(k).  Then x = r(1)/n(1) + r(2)/n(2) + r(3)/n(3) + ... , the r-Egyptian fraction for x. See A269993 for a guide to related sequences. LINKS Clark Kimberling, Table of n, a(n) for n = 1..11 Eric Weisstein's World of Mathematics, Egyptian Fraction EXAMPLE 1/e = 1/(2*2) + 1/(3*3) + 1/(4*37) + 1/(5*17282) + ... MATHEMATICA r[k_] := 1/(k+1); f[x_, 0] = x; z = 10; n[x_, k_] := n[x, k] = Ceiling[r[k]/f[x, k - 1]] f[x_, k_] := f[x, k] = f[x, k - 1] - r[k]/n[x, k] x = 1/E; Table[n[x, k], {k, 1, z}] CROSSREFS Cf. A269993. Sequence in context: A221055 A144466 A245061 * A119448 A041329 A060813 Adjacent sequences:  A270584 A270585 A270586 * A270588 A270589 A270590 KEYWORD nonn,frac,easy AUTHOR Clark Kimberling, Apr 03 2016 STATUS approved

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Last modified August 20 03:48 EDT 2019. Contains 326139 sequences. (Running on oeis4.)