A014013 Alternating Egyptian fraction expansion of Pi-3.

7, 790, 749896, 1270073831726, 3264508855407706377676178, 18710490702451568752627532846550947209438603938993

Offset: 1

Author

Simon Plouffe

Keywords

• nonn

Comments

The next term has 99 digits.

Examples

			1/(Pi - 3 - 1/7 + 1/790) = 749896.4427... hence a(3)=749896.
		

Links

• Index entries for sequences related to Egyptian fractions

Formula

Pi -3 = Sum_{k>=1} (-1)^(k+1)/a(k) = 0.14159...; a(n) = (-1)^(n+1)*u(n) where u(1)=7, u(n) = trunc(1/(Pi - 3 - Sum_{k=1..n-1} 1/u(k))) and trunc(x) = floor(x) if x >= 0, trunc(x) = ceiling(x) if x < 0.

Extensions

Title correction by Stanislav Sykora, May 05 2012