The On-Line Encyclopedia of Integer Sequences (OEIS)

A073834 revision #17

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

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

Table of n, a(n) for n=1..10.

Eric Weisstein's World of Mathematics, Fractional Chromatic Number

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 *)

PROG

(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 */

CROSSREFS

See A073833 for numerators.

Sequence in context: A098706 A143249 A161181 * A321267 A111837 A092123

Adjacent sequences: A073831 A073832 A073833 * A073835 A073836 A073837

KEYWORD

frac,nonn

AUTHOR

Alex Fink (finks(AT)telus.net), Aug 12 2002

STATUS

approved