A053520 Denominators of successive convergents to continued fraction 1/(2+2/(3+3/(4+4/(5+5/(6+6/(7+7/(8+8/9+...))))))).

2, 8, 38, 74, 1522, 11986, 11838, 1054766, 11506538, 45706526, 1772006854, 24681524038, 11169012898, 5874202721042, 99515904921182, 66139171377658, 3075946152109262, 51924337160029042, 4714400135799462226

Offset

0,1

Links

Table of n, a(n) for n=0..18.

M. A. Stern, Theorie der Kettenbrüche und ihre Anwendung, Crelle, 1832, pp. 1-22.

Example

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

Maple

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

Mathematica

a[n_] := ContinuedFractionK[k, k+1, {k, n+1}] // Denominator; Table[a[n], {n, 0, 18}] (* Jean-François Alcover, Mar 21 2016 *)

Crossrefs

Cf. A053518, A053519, A053556, A053557.

Sequence in context: A289316 A020130 A159051 * A202744 A112738 A220806

Adjacent sequences: A053517 A053518 A053519 * A053521 A053522 A053523

Keyword

nonn,frac,nice,easy

Author

N. J. A. Sloane, Jan 15 2000

Extensions

More terms from James A. Sellers, Feb 02 2000

Status

approved