A076658 Numerator of f(n), where for n > 2, f(n) = (n-1)/f(n-1) + (n-2)/f(n-2), with f(1)=1, f(2)=2.

1, 2, 2, 5, 31, 498, 8955, 2882938, 52586050459, 323804423976901335, 15495775772522155664701173463, 4775184376703288469595772730789093950647769107, 365485679191762741290548194655325571866478457308489227548407339087759232157

Offset

1,2

Comments

f(n)-> sqrt(2n), a slowly converging sequence.

The next term in the sequence (a(14)) has 120 digits. - Harvey P. Dale, Nov 29 2011

Links

Table of n, a(n) for n=1..13.

Example

f(3) = 2/f(2) + 1/f(1) = 2/2 + 1/1 = 2/1, so a(3) = 2.

Mathematica

Numerator[RecurrenceTable[{a[1]==1, a[2]==2, a[n]==(n-1)/a[n-1]+(n-2)/ a[n-2]}, a, {n, 13}]] (* Harvey P. Dale, Nov 29 2011 *)

Prog

(Maxima)
a[1]:1$
a[2]:2$
a[n]:=(n-1)/a[n-1]+(n-2)/a[n-2];
makelist(ratnumer(a[n]), n, 1, 15); /* Martin Ettl, Oct 30 2012 */

Crossrefs

Cf. A076659.

Sequence in context: A259861 A293264 A265777 * A218270 A218122 A282706

Adjacent sequences: A076655 A076656 A076657 * A076659 A076660 A076661

Keyword

nonn,frac

Author

Zak Seidov, Oct 24 2002

Extensions

One more term from Harvey P. Dale, Nov 29 2011

Status

approved