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 A274168 Number of real integers in n-th generation of tree T(r) defined in Comments, where r^2 = -r - 1 (i.e., r = (-1 + sqrt(3))/2). 1
 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 5, 5, 7, 9, 13, 18, 25, 33, 43 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Let T* be the infinite tree with root 0 generated by these rules:  if p is in T*, then p+1 is in T* and x*p is in T*.  Let g(n) be the set of nodes in the n-th generation, so that g(0) = {0}, g(1) = {1}, g(2) = {2,x}, g(3) = {3,2x,x+1,x^2}, etc.  Let T(r) be the tree obtained by substituting r for x. See A274142 for a guide to related sequences. LINKS EXAMPLE If r = (-1 + sqrt(3))/2), then g(3) = {3,2r,r+1, r^2}, in which the number of real integers is a(3) = 1. MATHEMATICA z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]]; u = Table[t[[k]] /. x -> (-1 + 3 I)/2, {k, 1, z}]; Table[ Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}] CROSSREFS Cf. A274142. Sequence in context: A027189 A140829 A184324 * A116575 A244800 A275972 Adjacent sequences:  A274165 A274166 A274167 * A274169 A274170 A274171 KEYWORD nonn,more AUTHOR Clark Kimberling, Jun 13 2016 STATUS approved

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Last modified July 6 23:56 EDT 2020. Contains 335484 sequences. (Running on oeis4.)