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A079278 Define b by b(1) = 1 and for n>1, b(n) = b(n-1)+1/(1+1/b(n-1)); sequence gives denominator of b(n). 6
1, 2, 10, 310, 363010, 594665194510, 1871071000515058250871610, 21362861761506953021644584296874581450310229239910 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

Suggested by Leroy Quet, Feb 14 2003.

LINKS

Table of n, a(n) for n=1..8.

FORMULA

Conjecture (Quet): a(m+1) = a(m)^2 + a(m)^3 /a(m-1)^2 - a(m)a(m-1)^2 for m >= 2.

EXAMPLE

The b sequence begins 1, 3/2, 21/10, 861/310, 1275141/363010, 2551762438701/594665194510, ...

MAPLE

b := proc(n) option remember; if n=1 then 1 else b(n-1)+1/(1+1/b(n-1)); fi; end;

MATHEMATICA

Denominator[NestList[#+1/(1+1/#)&, 1, 10]] (* Harvey P. Dale, Oct 07 2012 *)

CROSSREFS

Cf. A079269, A080581, A080582.

Sequence in context: A321267 A111837 A092123 * A275611 A015178 A296178

Adjacent sequences:  A079275 A079276 A079277 * A079279 A079280 A079281

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Feb 16 2003

EXTENSIONS

The next term is too large to include.

STATUS

approved

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Last modified May 20 12:33 EDT 2019. Contains 323422 sequences. (Running on oeis4.)