login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A270371 Denominators of r-Egyptian fraction expansion for sqrt(1/2), where r = (1,1/4,1/9,1/16,...). 1
2, 2, 2, 3, 7, 7702, 1234163819, 1590823281229385753, 7255753768720849630767399215373753335, 44436679763085787755205863082559307822924182270889047678247210478391618529 (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..13

Eric Weisstein's World of Mathematics, Egyptian Fraction

Index entries for sequences related to Egyptian fractions

EXAMPLE

sqrt(1/2) = 1/2 + 1/(4*2) + 1/(9*2) + 1/(16*3) + 1/(25*7) + ...

MATHEMATICA

r[k_] := 1/k^2; 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 = Sqrt[1/2]; Table[n[x, k], {k, 1, z}]

PROG

(PARI) r(k) = 1/k^2;

f(k, x) = if (k==0, x, f(k-1, x) - r(k)/a(k, x); );

a(k, x=sqrt(1/2)) = ceil(r(k)/f(k-1, x)); \\ Michel Marcus, Mar 21 2016

CROSSREFS

Cf. A269993.

Sequence in context: A200918 A134890 A101360 * A184311 A110910 A119532

Adjacent sequences:  A270368 A270369 A270370 * A270372 A270373 A270374

KEYWORD

nonn,frac,easy

AUTHOR

Clark Kimberling, Mar 20 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 July 12 08:23 EDT 2020. Contains 335657 sequences. (Running on oeis4.)