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A088559
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Decimal expansion of R^2 where R^2 is the real root of x^3+2*x^2+x-1=0.
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2
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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; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 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
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,20000
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FORMULA
| R^2=0.46557123187676... 1+R^2=1.46557123187676... = A092526 constant.
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PROG
| (PARI) { allocatemem(932245000); default(realprecision, 20080); x=10*solve(x=0, 1, x^3 + 2*x^2 + x - 1); for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b088559.txt", n, " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 21 2009]
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CROSSREFS
| Sequence in context: A062117 A200497 * A092526 A140243 A023825 A199289
Adjacent sequences: A088556 A088557 A088558 * A088560 A088561 A088562
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KEYWORD
| cons,nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 19 2003
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