A099876 Decimal expansion of a nested radical: sqrt(1! + sqrt(2! + sqrt(3! + ...

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

Offset: 1

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 02 2004

Keywords

• cons
• easy
• nonn

Examples

			1.82701471760859222637384319285...
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000
• Popular Computing (Calabasas, CA), The CSR Function, Vol. 4 (No. 34, Jan 1976), pages PC34-10 to PC34-11. Annotated and scanned copy.

Crossrefs

Cf. A072449, A099874.

Programs

Mathematica

RealDigits[Fold[Sqrt[#1 + #2] &, 0, Reverse[Range[100]!]], 10, 111][[1]]

PARI

t=0; forstep(n=300,1,-1,t=sqrt(t+n!)); t \\ gives more than enough correct digits for the number given here.