A073834 Denominators of b(n) where b(1) = 1, b(i) = b(i-1) + 1/b(i-1).

1, 1, 2, 10, 290, 272890, 264588959090, 268440386798659418988490, 295105036840595214385430531020664149472669868290, 377908709746050392481071609609580527436122569261424131112048023467330784739529329885668846964890

Offset: 1

Author

Alex Fink, Aug 12 2002

Keywords

• frac
• nonn

Comments

a(n) is also the denominator of the fractional chromatic number of the Mycielski graph M_n - Eric W. Weisstein, Mar 05 2011

References

• 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

Links

• Steven Finch, Popa's "Recurrent Sequences" and Reciprocity, arXiv:2412.11806 [math.CA], 2024. See p. 16.
• Eric Weisstein's World of Mathematics, Fractional Chromatic Number
• Eric Weisstein's World of Mathematics, Mycielski Graph

Crossrefs

See A073833 for numerators.

Programs

Mathematica

f[n_]:=n+1/n; Prepend[Denominator[NestList[f,2,9]],1] (* Vladimir Joseph Stephan Orlovsky, Nov 19 2010 *)
Denominator[NestList[# + 1/# &, 1, 10]] (* Eric W. Weisstein, Mar 05 2011 *)

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 */