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A270483 Denominators of r-Egyptian fraction expansion for 1/E, where r(k) = 1/Prime(k). 1
2, 3, 30, 1406, 1566618, 3968926143121, 51168240940958042671940949, 13365052216163708497107274374215341296314835773754330, 1279540722856331753015023627177246106080657069367343330334092565051020739543151941507268082633550601641928 (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..11

Eric Weisstein's World of Mathematics, Egyptian Fraction

Index entries for sequences related to Egyptian fractions

EXAMPLE

1/e = 1/(2*2) + 1/(3*3) + 1/(5*30) + 1/(7*1406) + ...

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

CROSSREFS

Cf. A269993, A000040.

Sequence in context: A137981 A110351 A326224 * A217370 A088115 A230627

Adjacent sequences:  A270480 A270481 A270482 * A270484 A270485 A270486

KEYWORD

nonn,frac,easy

AUTHOR

Clark Kimberling, Mar 30 2016

STATUS

approved

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Last modified July 16 04:26 EDT 2019. Contains 325064 sequences. (Running on oeis4.)