A010532 Decimal expansion of square root of 80.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Comments

Continued fraction expansion is 8 followed by {1, 16} repeated. - Harry J. Smith, Jun 09 2009

Examples

			8.944271909999158785636694674925104941762473438446102897083588981642083....
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• Index entries for algebraic numbers, degree 2

Crossrefs

Cf. A040071 (continued fraction). - Harry J. Smith, Jun 09 2009

Programs

Mathematica

RealDigits[Sqrt[80],10,120][[1]] (* Harvey P. Dale, Oct 20 2011 *)

PARI

default(realprecision, 20080); x=sqrt(80); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010532.txt", n, " ", d));  \\ Harry J. Smith, Jun 09 2009

Formula

From Amiram Eldar, Aug 02 2020: (Start)

Equals 10 * 2/sqrt(5) = 10 * Sum_{k>=0} (-1)^k * binomial(2*k,k)/16^k.

Equals 8 + Sum_{k>=0} (-1)^k * binomial(2*k,k)/((k+1) * 16^k). (End)

Extensions

Final digits of sequence corrected using the b-file. - N. J. A. Sloane, Aug 30 2009