A061083 - OEIS

%I #10 Mar 28 2014 21:23:59

%S 1,2,5,4,125,32,390625,8192,476837158203125,17179869184,

%T 277555756156289135105907917022705078125,618970019642690137449562112

%N Fibonacci-type sequence based on division: a(0) = 1, a(1) = 2 and a(n) = a(n-2)/a(n-1) but ignore decimal point.

%H Reinhard Zumkeller, <a href="/A061083/b061083.txt">Table of n, a(n) for n = 0..17</a>

%F a(n) = k^(n-th Fibonacci number) with k=2 if n is odd, k=5 if n is even

%e a(6) = 390625, since a(4)/a(5) = 125/32 = 3.90625

%o (Haskell)

%o a061083 n = a061083_list !! n

%o a061083_list = 1 : 2 : zipWith divIgnPnt a061083_list (tail a061083_list)

%o    where divIgnPnt x y = ddiv (10 * m) x' where

%o             ddiv u w | r == 0    = 10 * w + q

%o                      | otherwise = ddiv (10 * r) (10 * w + q)

%o                      where (q,r) = divMod u y

%o             (x',m) = divMod x y

%o -- _Reinhard Zumkeller_, Dec 29 2011

%Y Cf. A061084 for subtraction, A000301 for multiplication and A000045 for addition - the common Fibonacci numbers

%K nonn,easy,nice,base

%O 0,2

%A Ulrich Schimke (ulrschimke(AT)aol.com)