

A270586


Denominators of rEgyptian fraction expansion for Pi  3, where r(k) = 1/(k+1).


1



4, 21, 348, 160397, 27477992122, 8361728546142791039570, 65449866064796651219032701504776304475204846, 4242994078960802485293647297249599708082797742348261121304757890775884278785179376866443
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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(k1)), and f(k) = f(k1)  r(k)/n(k). Then x = r(1)/n(1) + r(2)/n(2) + r(3)/n(3) + ... , the rEgyptian fraction for x.
See A269993 for a guide to related sequences.


LINKS



EXAMPLE

Pi  3 = 1/(2*4) + 1/(3*21) + 1/(4*348) + 1/(5*160397) + ...


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 = Pi  3; Table[n[x, k], {k, 1, z}]


CROSSREFS



KEYWORD

nonn,frac,easy


AUTHOR



STATUS

approved



