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 A270486 Denominators of r-Egyptian fraction expansion for the Euler-Mascheroni constant (EulerGamma), where r(k) = 1/Prime(k). 1
 1, 5, 19, 6299, 29244983, 2480906174586499, 9602583972368431818444689851565, 310901734358858530002531740085708821780321504952699749074732105 (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..11 Eric Weisstein's World of Mathematics, Egyptian Fraction EXAMPLE Euler-Mascheroni constant = 1/(2*1) + 1/(3*5) + 1/(5*19) + 1/(7*6299) + ... MATHEMATICA r[k_] := 1/Prime[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 = EulerGamma; Table[n[x, k], {k, 1, z}] PROG (PARI) r(k) = 1/prime(k); f(k, x) = if (k==0, x, f(k-1, x) - r(k)/a(k, x); ); a(k, x=Euler) = ceil(r(k)/f(k-1, x)); \\ Michel Marcus, Mar 31 2016 CROSSREFS Cf. A269993, A000040. Sequence in context: A279256 A174490 A280034 * A278562 A013531 A122152 Adjacent sequences:  A270483 A270484 A270485 * A270487 A270488 A270489 KEYWORD nonn,frac,easy AUTHOR Clark Kimberling, Mar 30 2016 STATUS approved

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Last modified April 14 06:56 EDT 2021. Contains 342946 sequences. (Running on oeis4.)