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

1,1

Comments

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

Links

Harry J. Smith, Table of n, a(n) for n = 1..20000

Index entries for algebraic numbers, degree 2

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)

Example

8.944271909999158785636694674925104941762473438446102897083588981642083....

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A021532 A188638 A244664 * A317864 A335963 A243267

Adjacent sequences: A010529 A010530 A010531 * A010533 A010534 A010535

Keyword

nonn,cons

Author

N. J. A. Sloane

Extensions

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

Status

approved