A377968 Decimal expansion of tan(arctan(4)/4).

3, 4, 4, 1, 5, 0, 7, 3, 1, 4, 0, 8, 9, 1, 0, 8, 0, 7, 7, 1, 4, 7, 5, 9, 2, 2, 7, 8, 8, 5, 3, 4, 6, 8, 4, 7, 6, 0, 5, 6, 5, 0, 2, 0, 8, 3, 2, 5, 8, 4, 4, 0, 5, 8, 2, 4, 5, 8, 1, 7, 5, 1, 4, 8, 8, 0, 4, 5, 4, 0, 1, 0, 7, 8, 2, 8, 3, 5, 8, 4, 0, 3, 4, 3, 3, 3, 0, 5, 1, 0

Offset: 0

Author

Paolo Xausa, Nov 13 2024

Keywords

• nonn
• cons
• easy

Examples

			0.34415073140891080771475922788534684760565020832584...
		

Links

• Michael Penn, A beautiful identity, YouTube video, 2024.
• Index entries for algebraic numbers, degree 4

Crossrefs

Cf. A010473, A019684, A195628.

Programs

Mathematica

First[RealDigits[Tan[ArcTan[4]/4], 10, 100]]

Formula

Equals 2*(cos(6*Pi/17) + cos(10*Pi/17)) = 2*(cos(6*A019684) + cos(10*A019684)).

Equals (sqrt(34 + 2*sqrt(17)) - sqrt(17) - 1)/4 = (sqrt(34 + 2*A010473) - A010473 - 1)/4.

Equals the root closest to 0 of x^4 + x^3 - 6*x^2 - x + 1.