A061145 Sum of continued fraction terms in Sum_{k=1..n}(1/k^2).

1, 5, 10, 13, 26, 44, 53, 37, 47, 58, 60, 80, 198, 78, 115, 93, 206, 271, 1583, 144, 278, 235, 148, 185, 913, 366, 185, 215, 500, 251, 1002, 2127, 8704, 539, 546, 307, 636, 278, 3326, 290, 386, 665, 694, 313, 422, 364, 498, 455, 967, 748, 460, 731, 484, 1496, 2005

Offset

1,2

Links

Table of n, a(n) for n=1..55.

Example

1 + 1/2^2 + 1/3^2 = 49/36 = 1 + 1/(2 + 1/(1 + 1/(3 + 1/3))). So a(3) = 1 + 2 + 1 + 3 + 3 = 10.

Mathematica

Table[Sum[ContinuedFraction[Sum[1/i^2, {i, 1, n}]][[j]], {j, 1, Length[ContinuedFraction[Sum[1/i^2, {i, 1, n}]]]}], {n, 1, 80}] (* Stefan Steinerberger, Mar 24 2006 *)

Crossrefs

Sequence in context: A309593 A272267 A195735 * A345261 A321558 A328667

Adjacent sequences: A061142 A061143 A061144 * A061146 A061147 A061148

Keyword

easy,nonn

Author

Leroy Quet, May 29 2001

Extensions

More terms from Stefan Steinerberger, Mar 24 2006

Status

approved