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A089078
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Continued fraction for sqrt(2)+sqrt(3).
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4
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3, 6, 1, 5, 7, 1, 1, 4, 1, 38, 43, 1, 3, 2, 1, 1, 1, 1, 2, 4, 1, 4, 5, 1, 5, 1, 7, 22, 2, 5, 1, 1, 2, 1, 1, 31, 2, 1, 1, 3, 1, 44, 1, 89, 1, 8, 5, 2, 5, 1, 1, 4, 2, 8, 1, 17, 1, 4, 3, 4, 3, 2, 1, 1, 4, 2, 1, 9, 1, 15, 13, 1, 39, 20, 2, 152, 3, 2, 4, 1, 30, 1, 3, 1, 2, 1, 2, 16, 3, 24, 1, 9, 1, 172, 3, 1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| This is the most natural example of the fact that the sum of two periodic continued fractions need not have a periodic continued fraction.
a(n)=numbers of squares removed at stage n of the continued-fraction partitioning of a rectangle of length L and width W satisfying W=L*sqrt(8); see A188640. [From Clark Kimberling, Apr 13 2011]
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LINKS
| G. Xiao, Contfrac
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EXAMPLE
| 3.1462643699...
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MATHEMATICA
| r = 8^(1/2); t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]
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CROSSREFS
| Cf. A135611, A089078.
Sequence in context: A163327 A175032 A078768 * A134804 A145389 A055263
Adjacent sequences: A089075 A089076 A089077 * A089079 A089080 A089081
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KEYWORD
| cofr,nonn
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AUTHOR
| Jeppe Stig Nielsen (mail(AT)jeppesn.dk), Dec 04 2003
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