A015884 - OEIS

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A015884

A modified Pierce-type expansion for Pi: Pi = a(0)+Sum[ (-1)^Floor(n/2)/Product[a(i),{i,1,n}],{n,1,Infinity} ] = 3 + 1/7 - 1/7*113 - 1/7*113*4739 + 1/7*113*4739*46804 + 1/7*113*4739*46804*134370 - 1/7*113*4739*46804*134370*614063 - 1/7*113*4739*46804*134370*614063*1669512 + ...

3, 7, 113, 4739, 46804, 134370, 614063, 1669512, 15474115, 18858140, 19180902, 41486462, 492988666, 1794101482, 34644610027, 48670872793, 97414216753, 138669015304, 195575194804, 543142431219, 3173502039447, 4968328076747 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,1`
	LINKS	`Index entries for sequences related to Engel expansions`
	FORMULA	`a(0) = floor(Pi); A(1) = Pi-a(0); a(2n-1) = floor(1/A(2n-1)); A(2n) = 1-a(2n-1)A(2n-1); a(2n) = ceiling(1/A(2n)) and A(2n+1) = a(2n)A(2n)-1 for n >= 1.`
	CROSSREFS	`Cf. A061233.` `Sequence in context: A158467 A028414 A014014 * A156201 A066771 A139159` `Adjacent sequences: A015881 A015882 A015883 * A015885 A015886 A015887`
	KEYWORD	`nonn`
	AUTHOR	`Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), Jun 02 2000`
	EXTENSIONS	`Better description and more terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 28 2001`

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Last modified February 16 01:56 EST 2012. Contains 205860 sequences.