

A270546


Denominators of rEgyptian fraction expansion for sqrt(1/2), where r(k) = 1/(2k1).


2



2, 2, 5, 325, 200533, 65627675599, 22975481891957121466348, 1958997403653886589078102754522745217186637162, 141280756113351994103874857935521871912536028357392961997286697261498102983722388787617517574
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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

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

sqrt(1/2) = 1/(1*2) + 1/(3*2) + 1/(5*5) + 1/(7*325) + ...


MATHEMATICA

r[k_] := 1/(2k1); 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/(2*k1);
f(k, x) = if (k==0, x, f(k1, x)  r(k)/a(k, x); );
a(k, x=sqrt(1/2)) = ceil(r(k)/f(k1, x)); \\ Michel Marcus, Apr 03 2016


CROSSREFS

Cf. A269993, A005408, A010503.
Sequence in context: A036739 A158311 A158061 * A163119 A091085 A011144
Adjacent sequences: A270543 A270544 A270545 * A270547 A270548 A270549


KEYWORD

nonn,frac,easy


AUTHOR

Clark Kimberling, Apr 02 2016


STATUS

approved



