A384806 Simple continued fraction expansion of arctan(1/2)/Pi.

0, 6, 1, 3, 2, 5, 1, 6, 5, 3, 1, 1, 2, 1, 1, 2, 3, 1, 2, 3, 2, 2, 2, 2, 3, 2, 1, 1, 3, 1, 3, 2, 1, 1, 3, 1, 17, 1, 5, 1, 2, 1, 2, 1, 1, 1, 1, 4, 7, 11, 1, 2, 1, 583, 1, 2, 1, 1, 2, 22, 7, 3, 23, 2, 6, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 5, 1, 1, 2, 3, 17, 6, 2, 70, 1, 6

Offset: 0

Author

Stefano Spezia, Jun 10 2025

Keywords

• nonn
• cofr

Examples

			arctan(1/2)/Pi = 1/(6 + 1/(1 + 1/(3 + 1/(2 + 1/(5 + ... ))))).
		

Links

• Shigeki Akiyama, Emily R. Korfanty, and Yan-li Xu, Delone sets associated with badly approximable triangles, Journal of Number Theory, (2025).
• Index entries for continued fractions for constants.

Crossrefs

Cf. A000796, A073000, A086203 (decimal expansion).

Programs

Mathematica

ContinuedFraction[ArcTan[1/2]/Pi,90]