A110483 Continued fraction for seventh root of 2.

1, 9, 1, 1, 1, 1, 5, 46, 1, 3, 2, 1, 1, 3, 1, 1, 2, 1, 22, 48, 1, 1, 5, 4, 1, 1, 1, 1, 1, 1, 2, 8, 1, 6, 1, 21, 1, 1, 1, 1, 1, 6, 1, 1, 3, 3, 1, 1, 2, 2, 2, 3, 1, 26, 1, 16, 1, 4, 21, 1, 2, 1, 1, 1, 5, 3, 7, 21, 3, 1, 1, 1, 8, 1, 8, 1, 4, 1, 24, 1, 3, 1, 6, 1, 2, 1, 5, 5, 6, 1, 12, 1, 8, 2, 2, 1, 3, 1, 1, 2

Offset: 0

Author

Paul Stoeber (pstoeber(AT)uni-potsdam.de), Sep 09 2005

Keywords

• cofr
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A002945, A002950.

Programs

Haskell

import Ratio
floorRoot :: Integer -> Integer -> Integer
floorRoot k n | k>=1 && n>=1 = h n where h x = let y=((k-1)*x+n`div`x^(k-1))`div`k in if y (Integer,Rational)
intFrac x = let ((a,b),~(q,r)) = ((numerator x,denominator x),divMod a b) in (q,r%b)
cf :: Rational -> Rational -> [Integer]
cf x y = let ((xi,xf),(yi,yf)) = (intFrac x,intFrac y) in if xi==yi then xi : cf (recip xf) (recip yf) else []
y = 2^512 -- increase to get more terms, decrease to get a quick answer
(k,n) = (7,2) -- compute continued fraction for k-th root of n
main = print (let x = floorRoot k (n*y^k) in cf (x%y) ((x+1)%y))

Mathematica

ContinuedFraction[Surd[2,7],100] (* Harvey P. Dale, Aug 11 2017 *)