A052385 - OEIS

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A052385

a(n)*10^n are the denominators of the greedy alternating Egyptian fraction expansion of Pi - 3 of the form Sum_{n>=0} (-1)^n / (a(n)*10^n).

7, 79, 7498, 5830114, 8652011824287, 13597204960705459608723126, 34810495772672927583903155370200945603822050731477, 1443540369391032855921234984363709782471552979298036142515612532020988429757781997263178546460721652

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

LINKS

Amiram Eldar, Table of n, a(n) for n = 0..10

FORMULA

a(n) = floor((-1)^n/(s(n-1)*10^n)), where s(n) = Pi - 3 - Sum_{k=0..n} (-1)^k/(a(k)*10^k).

EXAMPLE

Pi = 3 + 1/7 - 1/(10 * 79) + 1/(10^2 * 7498) - 1/(10^3 * 5830114) + ...

MATHEMATICA

s={}; x = Pi - 3; Do[a = Floor[1/((-10)^k * x)]; AppendTo[s, a]; x-=1/((-10)^k*a), {k, 0, 7}]; s (* Amiram Eldar, Jan 23 2019 *)

CROSSREFS