login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A053520 Denominators of successive convergents to continued fraction 1/(2+2/(3+3/(4+4/(5+5/(6+6/(7+7/(8+8/9+...))))))). 5

%I

%S 2,8,38,74,1522,11986,11838,1054766,11506538,45706526,1772006854,

%T 24681524038,11169012898,5874202721042,99515904921182,66139171377658,

%U 3075946152109262,51924337160029042,4714400135799462226

%N Denominators of successive convergents to continued fraction 1/(2+2/(3+3/(4+4/(5+5/(6+6/(7+7/(8+8/9+...))))))).

%D M. A. Stern, Theorie der Kettenbr├╝che und ihre Anwendung, Crelle, 1832, pp. 1-22.

%e Convergents are 1/2, 3/8, 15/38, 29/74, 597/1522, 4701/11986, ...

%p for j from 1 to 50 do printf(`%d,`,denom(cfrac([0,seq([i,i+1],i=1..j)]))); od:

%t a[n_] := ContinuedFractionK[k, k+1, {k, n+1}] // Denominator; Table[a[n], {n, 0, 18}] (* _Jean-Fran├žois Alcover_, Mar 21 2016 *)

%Y Cf. A053518, A053519, A053556, A053557.

%K nonn,frac,nice,easy

%O 0,1

%A _N. J. A. Sloane_, Jan 15 2000

%E More terms from _James A. Sellers_, Feb 02 2000

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 11 04:17 EST 2016. Contains 279034 sequences.