A270590 Denominators of r-Egyptian fraction expansion for the Euler-Mascheroni constant (EulerGamma), where r(k) = 1/(k+1).

1, 5, 24, 1512, 2953202, 23271987449429, 695674431250515976519182860, 5836770961962275507879845242138280180068525903243835399, 252105542081571496083070310148809536964991357782450789266426812999313566935591332769492328764874678005359339022

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

Index entries for sequences related to Egyptian fractions

Example

Euler-Mascheroni constant = 1/(2*1) + 1/(3*5) + 1/(4*24) + 1/(5*1512) + ...

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 = EulerGamma; Table[n[x, k], {k, 1, z}]

Crossrefs

Cf. A269993.

Sequence in context: A270581 A156310 A142725 * A271378 A305837 A175555

Adjacent sequences: A270587 A270588 A270589 * A270591 A270592 A270593

Keyword

nonn,frac,easy

Author

Clark Kimberling, Apr 04 2016

Status

approved