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

0,2

Links

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

Mathematica

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

Prog

(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<x then h y else x
intFrac :: Rational -> (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))

Crossrefs

Cf. A002945, A002950.

Sequence in context: A087966 A087968 A340365 * A348734 A010164 A006084

Adjacent sequences: A110480 A110481 A110482 * A110484 A110485 A110486

Keyword

cofr,nonn

Author

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

Status

approved