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

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

Cf. A000796, A001466, A014013.

Sequence in context: A267798 A201704 A331424 * A093947 A222137 A115986

Adjacent sequences: A052382 A052383 A052384 * A052386 A052387 A052388

Keyword

easy,frac,nonn

Author

Boris Gourevitch (sai1042(AT)ensai.fr), Mar 10 2000

Extensions

a(6)-a(10) from Amiram Eldar, Jan 23 2019

Status

approved