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

Author

N. J. A. Sloane, Jan 15 2000

Keywords

• nonn
• frac
• nice
• easy

Examples

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

Links

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

Crossrefs

Cf. A053518, A053519, A053556, A053557.

Programs

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 *)

Extensions

More terms from James Sellers, Feb 02 2000