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A073833
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Numerators of b(n) where b(1) = 1, b(i) = b(i-1) + 1/b(i-1).
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3
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1, 2, 5, 29, 941, 969581, 1014556267661, 1099331737522548368039021, 1280590510388959061548230114212510564911731118541, 1726999038066943724857508638586386504281539279376091034086485112150121338989977841573308941492781
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OFFSET
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1,2
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COMMENTS
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Lim n -> infinity (1/n)*exp(2*(b(n)^2-2n)) = c = 0.57...... - Benoit Cloitre, Oct 16 2002
a(n) is also the numerator of the fractional chromatic number of the Mycielski graph M_n - Eric W. Weisstein, Mar 05 2011
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REFERENCES
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H. L. Montgomery, Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis, Amer. Math. Soc., 1996, p. 187.
D. J. Newman, A Problem Seminar, Springer; see Problem #60.
J. H. Silverman, The arithmetic of dynamical systems, Springer, 2007, see p. 113 Table 3.1
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LINKS
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Table of n, a(n) for n=1..10.
Eric Weisstein's World of Mathematics, Fractional Chromatic Number
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FORMULA
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a(n) = a(n-1)^2 + A073834(n-1)^2; A073834(n) = a(n-1) * A073834(n-1). [From Franklin T. Adams-Watters, Aug 04 2008]
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EXAMPLE
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1, 2, 5/2, 29/10, 941/290, 969581/272890, 1014556267661/264588959090, 1099331737522548368039021/268440386798659418988490, ...
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MATHEMATICA
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f[n_]:=n+1/n; Prepend[Numerator[NestList[f, 2, 9]], 1] [From Vladimir Joseph Stephan Orlovsky, 2010Nov19]
Numerator[NestList[# + 1/# &, 1, 10]] [From Eric W. Weisstein, 5 Mar 2001]
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PROG
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(PARI) {a(n) = local(x, y); if( n<1, 0, if( n<3, n, x = a(n-2)^2; y = a(n-1); y^2 + x * (y - x)))} /* Michael Somos, Mar 05 2012 */
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CROSSREFS
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See A073834 for denominators.
Sequence in context: A059784 A000283 A121910 * A179554 A086383 A118612
Adjacent sequences: A073830 A073831 A073832 * A073834 A073835 A073836
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KEYWORD
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frac,nonn
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AUTHOR
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Alex Fink (finks(AT)telus.net), Aug 12 2002
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STATUS
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approved
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