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A110483 Continued fraction for seventh root of 2.

%I A110483 #9 Aug 29 2017 19:10:56
%S A110483 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,
%T A110483 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,
%U A110483 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
%N A110483 Continued fraction for seventh root of 2.
%H A110483 G. C. Greubel, <a href="/A110483/b110483.txt">Table of n, a(n) for n = 0..5000</a>
%t A110483 ContinuedFraction[Surd[2,7],100] (* _Harvey P. Dale_, Aug 11 2017 *)
%o A110483 (Haskell) import Ratio
%o A110483 floorRoot :: Integer -> Integer -> Integer
%o A110483 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
%o A110483 intFrac :: Rational -> (Integer,Rational)
%o A110483 intFrac x = let ((a,b),~(q,r)) = ((numerator x,denominator x),divMod a b) in (q,r%b)
%o A110483 cf :: Rational -> Rational -> [Integer]
%o A110483 cf x y = let ((xi,xf),(yi,yf)) = (intFrac x,intFrac y) in if xi==yi then xi : cf (recip xf) (recip yf) else []
%o A110483 y = 2^512 -- increase to get more terms, decrease to get a quick answer
%o A110483 (k,n) = (7,2) -- compute continued fraction for k-th root of n
%o A110483 main = print (let x = floorRoot k (n*y^k) in cf (x%y) ((x+1)%y))
%Y A110483 Cf. A002945, A002950.
%K A110483 cofr,nonn
%O A110483 0,2
%A A110483 Paul Stoeber (pstoeber(AT)uni-potsdam.de), Sep 09 2005