# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a281426 Showing 1-1 of 1 %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, Table of n, a(n) for n = 1..1000 %H A281426 Rémy Sigrist, PARI program for A281426 %H A281426 Rémy Sigrist, Scatterplot of A232890 vs A281426 for n=1..10000 %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 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE