A102367 (Numerator of n-th convergent to Pi having an even numerator)/2.

11, 52174, 573204, 122925461, 534483448, 3083975227, 2685575996367, 214112296674652, 131226315167691099699, 396325638628212603442, 5947531272548328355975, 118554299812338354516058

Offset

1,1

Comments

Abs[Cos[a(n)]] approaches 0; Abs[Sin[a(n)]] approaches 1.

Links

Table of n, a(n) for n=1..12.

Eric Weisstein's World of Mathematics, Convergent.

Example

a(1) = 11 because the first convergent of Pi with an even numerator is 22/7.

Mathematica

Select[Table[1/2*Numerator[FromContinuedFraction[ContinuedFraction[Pi, k][[Range[1, k]]]]], {k, 1, 60}], IntegerQ]

Crossrefs

Cf. A000796, A002485.

Sequence in context: A343119 A295176 A337248 * A055322 A348644 A165934

Adjacent sequences: A102364 A102365 A102366 * A102368 A102369 A102370

Keyword

base,nonn

Author

Joseph Biberstine (jrbibers(AT)indiana.edu), Feb 22 2005

Status

approved