id:A088559 - OEIS Search Results

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Decimal expansion of R^2 where R is the real root of x^3+2*x^2+x-1=0.

+0
2

4, 6, 5, 5, 7, 1, 2, 3, 1, 8, 7, 6, 7, 6, 8, 0, 2, 6, 6, 5, 6, 7, 3, 1, 2, 2, 5, 2, 1, 9, 9, 3, 9, 1, 0, 8, 0, 2, 5, 5, 7, 7, 5, 6, 8, 4, 7, 2, 2, 8, 5, 7, 0, 1, 6, 4, 3, 1, 8, 3, 1, 1, 1, 2, 4, 9, 2, 6, 2, 9, 9, 6, 6, 8, 5, 0, 1, 7, 8, 4, 0, 4, 7, 8, 1, 2, 5, 8, 0, 1, 1, 9, 4, 9, 0, 9, 2, 7, 0, 0, 6, 4, 3, 8 (list; cons; graph; listen)

	OFFSET	`0,1`
	COMMENT	`Arise in a study of AGM (arithmetic-geometric mean) and HGM (harmonic-geometric mean) - like sequences. Let u(k+1)=sqrt(u(k)v(k)); v(k+1)=v(k)+u(k) and r(k+1)=sqrt(r(k)s(k)); s(k+1)=1/(1/r(k)+1/s(k)). Then for any positive initial values u(0),v(0),r(0),s(0) limit k-->infty u(k)/v(k)= limit k-->infty s(k)/r(k)=R^2`
	FORMULA	`R^2=0.46557123187676... 1+R^2=1.46557123187676... = A092526 constant.`
	CROSSREFS	`Sequence in context: A021219 A002245 A062117 this_sequence A092526 A140243 A023825` `Adjacent sequences: A088556 A088557 A088558 this_sequence A088560 A088561 A088562`
	KEYWORD	`cons,nonn`
	AUTHOR	`Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 19 2003`

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Last modified September 6 16:04 EDT 2008. Contains 143483 sequences.

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