id:A014013 - OEIS Search Results

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Alternating Egyptian fraction expansion of Pi.

+0
3

7, 790, 749896, 1270073831726, 3264508855407706377676178, 18710490702451568752627532846550947209438603938993, 973885998866223812020176506328879365154595266536880449064639606785601754387311047869879785998363014 (list; graph; listen)

	OFFSET	`1,1`
	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)=ceil(x) if x<0`
	EXAMPLE	`1/(Pi-3-1/7+1/790) = 749896.4427... hence a(3)=749896`
	CROSSREFS	`Sequence in context: A137050 A114911 A020470 this_sequence A001467 A047788 A087350` `Adjacent sequences: A014010 A014011 A014012 this_sequence A014014 A014015 A014016`
	KEYWORD	`nonn`
	AUTHOR	`Simon Plouffe (plouffe(AT)math.uqam.ca)`

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Last modified August 29 17:54 EDT 2008. Contains 143238 sequences.

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