A081478 - OEIS

%I #27 Oct 11 2021 18:45:12

%S 1,2,2,-2,6,-6,42,-42,1806,-1806,3263442,-3263442,10650056950806,

%T -10650056950806,113423713055421844361000442,

%U -113423713055421844361000442,12864938683278671740537145998360961546653259485195806

%N Consider the mapping f(a/b) = (a - b)/(ab). Taking a = 2 and b = 1 to start with and carrying out this mapping repeatedly on each new (reduced) rational number gives the following sequence 2/1,1/2,-1/2,-3/-2,-1/6,... Sequence contains the denominators.

%C The mapping f(a/b) = (a + b)/(a - b). Taking a = 2 and b = 1 to start with and carrying out this mapping repeatedly on each new (reduced) rational number gives the periodic sequence 2/1,3/1,2/1,3/1,...

%H Seiichi Manyama, <a href="/A081478/b081478.txt">Table of n, a(n) for n = 1..26</a>

%F a(2n-1) = A007018(n-1), a(2n) = -A007018(n-1) for n >= 2. - _Jianing Song_, Oct 10 2021

%t Last /@ NestList[{(#1 - #2), #1 #2} & @@ # &, {2, 1}, 16] (* _Michael De Vlieger_, Sep 04 2016 *)

%o (Sage)

%o # Variant with first four terms slightly different. Absolute values.

%o def A081478_abs():

%o     x, y = 1, 2

%o     yield x

%o     while True:

%o        yield x

%o        x, y = x * y, x//y + 1

%o a = A081478_abs(); print([next(a) for i in range(17)])  # _Peter Luschny_, Dec 17 2015

%Y A003687 gives the numerators.

%Y Cf. A007018.

%K sign,frac

%O 1,2

%A _Amarnath Murthy_, Mar 24 2003

%E More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003