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 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+...))))))).

%H M. A. Stern, <a href="http://gdz.sub.uni-goettingen.de/dms/load/img/?PID=GDZPPN002138999">Theorie der Kettenbrüche und ihre Anwendung</a>, 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-François 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

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