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 A270588 Denominators of r-Egyptian fraction expansion for e - 2, where r(k) = 1/(k+1). 1
 1, 2, 5, 124, 73794, 5284326699, 229125959519570751554, 95635936955933623982265743051662580385628, 16608415739298461036456146606021108793638909234932647123655496824423388126111599755 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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..12 Eric Weisstein's World of Mathematics, Egyptian Fraction EXAMPLE e - 2 = 1/(2*1) + 1/(3*2) + 1/(4*5) + 1/(5*124) + ... 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 = E - 2; Table[n[x, k], {k, 1, z}] CROSSREFS Cf. A269993. Sequence in context: A276109 A270481 A225944 * A214648 A175978 A092922 Adjacent sequences:  A270585 A270586 A270587 * A270589 A270590 A270591 KEYWORD nonn,frac,easy AUTHOR Clark Kimberling, Apr 03 2016 STATUS approved

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Last modified October 21 19:29 EDT 2019. Contains 328315 sequences. (Running on oeis4.)