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 A003687 a(n+1) = a(n)-a(1)a(2)...a(n-1), if n>0. a(0)=1, a(1)=2. 4
 1, 2, 1, -1, -3, -1, -7, -1, -43, -1, -1807, -1, -3263443, -1, -10650056950807, -1, -113423713055421844361000443, -1, -12864938683278671740537145998360961546653259485195807, -1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) = a(n-1)-a(n-2)^2+a(n-1)*a(n-2), if n>2. - Michael Somos, Mar 19 2004 Consider the mapping f(a/b) = (a - b)/(ab). Taking a = 2 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 numerators. - Amarnath Murthy, Mar 24 2003 An infinite coprime sequence defined by recursion. - Michael Somos, Mar 19 2004 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..27 MATHEMATICA {1}~Join~NestList[{(#1 - #2), #1 #2} & @@ # &, {2, 1}, 17] [[All, 1]] (* Michael De Vlieger, Sep 04 2016 *) PROG (PARI) a(n)=local(an); if(n<1, (n==0), an=vector(max(2, n)); an[1]=2; an[2]=1; for(k=3, n, an[k]=an[k-1]-an[k-2]^2+an[k-1]*an[k-2]); an[n]) (Sage) def A003687():     x, y = 2, 1     yield y     while true:        yield x        x, y = x - y, x * y a = A003687(); print([next(a) for i in range(20)])  # Peter Luschny, Dec 17 2015 (MAGMA) I:=[1, 2, 1]; [n le 3 select I[n] else Self(n-1)-Self(n-2)^2+Self(n-1)*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Dec 17 2015 CROSSREFS Cf. A081478. For n>1, a(2n-1) = -1, a(2n) = -A007018(n-1) - 1. Sequence in context: A277606 A228267 A170820 * A104575 A318833 A173937 Adjacent sequences:  A003684 A003685 A003686 * A003688 A003689 A003690 KEYWORD sign,easy AUTHOR STATUS approved

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Last modified June 4 08:18 EDT 2020. Contains 334825 sequences. (Running on oeis4.)