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A274165 Number of real integers in n-th generation of tree T(i/3) defined in Comments.

%I A274165 #18 Mar 16 2022 02:49:21
%S A274165 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,
%T A274165 57,67,79,93,110,131,157,189,228,276,332,399,478,571,681,812,969,1158,
%U A274165 1387,1662,1994,2393,2871,3442,4123,4935,5904,7063,8449,10111
%N A274165 Number of real integers in n-th generation of tree T(i/3) defined in Comments.
%C A274165 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.
%C A274165 See A274142 for a guide to related sequences.
%C A274165 a(n) = A017885(n+7) for 2 <= n < 85, but a(85) = 1314173 differs from A017885(92) = 1314172. - _Georg Fischer_, Oct 30 2018
%H A274165 Kenny Lau, <a href="/A274165/b274165.txt">Table of n, a(n) for n = 0..4727</a>
%e A274165 If r = i/3, then g(3) = {3,2r,r+1, r^2}, in which the number of real integers is a(3) = 1.
%t A274165 z = 18; t = Join[{{0}}, Expand[NestList[DeleteDuplicates[Flatten[Map[{# + 1, x*#} &, #], 1]] &, {1}, z]]];
%t A274165 u = Table[t[[k]] /. x -> I/3, {k, 1, z}]; Table[Count[Map[IntegerQ, u[[k]]], True], {k, 1, z}]
%Y A274165 Cf. A274142.
%K A274165 nonn
%O A274165 0,12
%A A274165 _Clark Kimberling_, Jun 12 2016
%E A274165 More terms from _Kenny Lau_, Jun 30 2017