A283749 Decimal expansion of the limit of the nested sin(1+ sin(2+ sin(3+ sin(4+ ...)))).

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

Offset: 0

Author

Alex Klotz and Robert G. Wilson v, Mar 15 2017

Keywords

• cons
• nonn

Comments

In radians.

No closed form expression is known.

Probably transcendental but this has not been proved.

By Lindemann's theorem, at most one of sin(1+ sin(2+ sin(3+...))) and sin(2+ sin(3+ sin(4+ ...))) is algebraic. - Robert Israel, Mar 15 2017

Examples

			0.9941666781206763386906217886955585128252297434319229865047087903224658848...
		

Crossrefs

Cf. A072449, A277313.

Programs

Mathematica

RealDigits[Fold[ Sin[#1 + #2] &, 0, Reverse[Range[284]]], 10, 111][[1]]