cp's OEIS Frontend

A281426 Numerator of n-th term of sequence (or tree) S of all rational numbers generated by these rules: 0 is in S; if x is in S then x + 1 is in S, and if x + 1 is nonzero, then -1/(x + 1) is in S; duplicates are deleted as they occur.

%I A281426 #14 Oct 07 2017 13:07:34
%S A281426 0,1,-1,2,-1,3,-1,1,-2,4,-1,2,-3,3,-2,5,-1,3,-4,5,-3,5,-2,1,-3,6,-1,4,
%T A281426 -5,7,-4,8,-3,2,-5,7,-2,3,-5,4,-3,7,-1,5,-6,9,-5,11,-4,3,-7,11,-3,5,
%U A281426 -8,7,-5,9,-2,5,-7,8,-5,7,-3,1,-4,8,-1,6,-7,11,-6,14
%N A281426 Numerator of n-th term of sequence (or tree) S of all rational numbers generated by these rules:  0 is in S; if x is in S then x + 1 is in S, and if x + 1 is nonzero, then -1/(x + 1) is in S; duplicates are deleted as they occur.
%C A281426 See A232890 for the corresponding denominators and additional comments.
%H A281426 Rémy Sigrist, <a href="/A281426/b281426.txt">Table of n, a(n) for n = 1..1000</a>
%H A281426 Rémy Sigrist, <a href="/A281426/a281426.gp.txt">PARI program for A281426</a>
%H A281426 Rémy Sigrist, <a href="/A281426/a281426.png">Scatterplot of A232890 vs A281426 for n=1..10000</a>
%e A281426 To generate S, the number 0 begets (1,-1), whence 1 begets 2 and -1/2, whereas -1 begets 0 and -1/2, both of which are (deleted )duplicates, so that g(3) = (2, -1/2).  The resulting concatenation of all the generations g(n) begins with 0, 1, -1, 2, -1/2, 3, -1/3, 1/2, -2, 4, -1/4, so that A232890 begins with 0, 1, -1, 2, -1, 3, -1, 1, -2, 4.
%o A281426 (PARI) See Links section.
%Y A281426 Cf. A232559, A232890.
%K A281426 frac,sign
%O A281426 1,4
%A A281426 _Rémy Sigrist_, Oct 05 2017