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 A269998 Denominators of r-Egyptian fraction expansion for 1/Pi, where r = (1,1/2,1/3,1/4,...) 2
 4, 8, 58, 3984, 22875462, 931267108879599, 1031674577884217945682977326053, 1260295551033259417770370489346530643885445465368122822066849 (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..12 Eric Weisstein's World of Mathematics, Egyptian Fraction EXAMPLE 1/Pi = 1/4 + 1/(2*8) + 1/(3*58) + ... MATHEMATICA r[k_] := 1/k; 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/Pi; Table[n[x, k], {k, 1, z}] PROG (PARI) r(k) = 1/k; x = 1/Pi; f(x, k) = if(k<1, x, f(x, k - 1) - r(k)/n(x, k)); n(x, k) = ceil(r(k)/f(x, k - 1)); for(k = 1, 8, print1(n(x, k), ", ")) \\ Indranil Ghosh, Mar 29 2017 CROSSREFS Cf. A269993. Sequence in context: A192200 A063083 A270399 * A303284 A275574 A214590 Adjacent sequences:  A269995 A269996 A269997 * A269999 A270000 A270001 KEYWORD nonn,frac,easy AUTHOR Clark Kimberling, Mar 15 2016 STATUS approved

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Last modified January 21 21:30 EST 2020. Contains 331128 sequences. (Running on oeis4.)