%I #22 May 06 2022 07:37:09

%S 1,1,2,10,290,272890,264588959090,268440386798659418988490,

%T 295105036840595214385430531020664149472669868290,

%U 377908709746050392481071609609580527436122569261424131112048023467330784739529329885668846964890

%N Denominators of b(n) where b(1) = 1, b(i) = b(i-1) + 1/b(i-1).

%C a(n) is also the denominator of the fractional chromatic number of the Mycielski graph M_n - _Eric W. Weisstein_, Mar 05 2011

%D H. L. Montgomery, Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis, Amer. Math. Soc., 1996, p. 187.

%D D. J. Newman, A Problem Seminar, Springer; see Problem #60.

%D J. H. Silverman, The arithmetic of dynamical systems, Springer, 2007, see p. 113 Table 3.1

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FractionalChromaticNumber.html">Fractional Chromatic Number</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MycielskiGraph.html">Mycielski Graph</a>

%t f[n_]:=n+1/n; Prepend[Denominator[NestList[f,2,9]],1] (* _Vladimir Joseph Stephan Orlovsky_, Nov 19 2010 *)

%t Denominator[NestList[# + 1/# &, 1, 10]] (* _Eric W. Weisstein_, Mar 05 2011 *)

%o (PARI) {a(n) = local(x, y); if( n<1, 0, if( n<3, n, x = a(n-2)^2; y = a(n-1); y*y + x * (y - x)))} /* _Michael Somos_, Mar 05 2012 */

%Y See A073833 for numerators.

%K frac,nonn

%O 1,3

%A _Alex Fink_, Aug 12 2002