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A081478 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.

%I A081478 #27 Oct 11 2021 18:45:12
%S A081478 1,2,2,-2,6,-6,42,-42,1806,-1806,3263442,-3263442,10650056950806,
%T A081478 -10650056950806,113423713055421844361000442,
%U A081478 -113423713055421844361000442,12864938683278671740537145998360961546653259485195806
%N A081478 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 A081478 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 A081478 Seiichi Manyama, <a href="/A081478/b081478.txt">Table of n, a(n) for n = 1..26</a>
%F A081478 a(2n-1) = A007018(n-1), a(2n) = -A007018(n-1) for n >= 2. - _Jianing Song_, Oct 10 2021
%t A081478 Last /@ NestList[{(#1 - #2), #1 #2} & @@ # &, {2, 1}, 16] (* _Michael De Vlieger_, Sep 04 2016 *)
%o A081478 (Sage)
%o A081478 # Variant with first four terms slightly different. Absolute values.
%o A081478 def A081478_abs():
%o A081478     x, y = 1, 2
%o A081478     yield x
%o A081478     while True:
%o A081478        yield x
%o A081478        x, y = x * y, x//y + 1
%o A081478 a = A081478_abs(); print([next(a) for i in range(17)])  # _Peter Luschny_, Dec 17 2015
%Y A081478 A003687 gives the numerators.
%Y A081478 Cf. A007018.
%K A081478 sign,frac
%O A081478 1,2
%A A081478 _Amarnath Murthy_, Mar 24 2003
%E A081478 More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003