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 A274165 Number of real integers in n-th generation of tree T(i/3) defined in Comments. 2
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 14, 17, 21, 26, 32, 39, 47, 57, 67, 79, 93, 110, 131, 157, 189, 228, 276, 332, 399, 478, 571, 681, 812, 969, 1158, 1387, 1662, 1994, 2393 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,12 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. a(n) = A017885(n+7) for 2 <= n < 85, but a(85) = 1314173 differs from A017885(92) = 1314172. - Georg Fischer, Oct 30 2018 LINKS Kenny Lau, Table of n, a(n) for n = 0..4727 EXAMPLE If r = i/3, 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 -> I/3, {k, 1, z}]; Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}] CROSSREFS Cf. A274142. Sequence in context: A017896 A118868 A017885 * A011874 A000115 A033552 Adjacent sequences:  A274162 A274163 A274164 * A274166 A274167 A274168 KEYWORD nonn,more AUTHOR Clark Kimberling, Jun 12 2016 EXTENSIONS More terms from Kenny Lau, Jun 30 2017 STATUS approved

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Last modified January 18 13:09 EST 2019. Contains 319271 sequences. (Running on oeis4.)