

A270483


Denominators of rEgyptian fraction expansion for 1/E, where r(k) = 1/Prime(k).


1



2, 3, 30, 1406, 1566618, 3968926143121, 51168240940958042671940949, 13365052216163708497107274374215341296314835773754330, 1279540722856331753015023627177246106080657069367343330334092565051020739543151941507268082633550601641928
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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

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



KEYWORD

nonn,frac,easy


AUTHOR



STATUS

approved



