login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A270526 Denominators of r-Egyptian fraction expansion for the Euler-Mascheroni constant (EulerGamma), where r(k) = 1/k!. 1
2, 7, 29, 1043, 458614, 38061814595, 589807060799058309509, 90876245982275966864729604588044176066410, 3391075284415616236534347480596844341262253542409106867347953764596067404012977402 (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

Index entries for sequences related to Egyptian fractions

EXAMPLE

Euler-Mascheroni constant = 1/(1*2) + 1/(2*7) + 1/(6*29) + 1/(24*1043) + ...

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

PROG

(PARI) r(k) = 1/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, A000142, A001620.

Sequence in context: A094475 A093034 A125174 * A037417 A042913 A041805

Adjacent sequences:  A270523 A270524 A270525 * A270527 A270528 A270529

KEYWORD

nonn,frac,easy

AUTHOR

Clark Kimberling, Mar 30 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 25 23:48 EDT 2019. Contains 322465 sequences. (Running on oeis4.)