

A274165


Number of real integers in nth 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
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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 nth 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



