login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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.

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,easy

AUTHOR

Clark Kimberling, Jun 12 2016

EXTENSIONS

More terms from Kenny Lau, Jun 30 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 20 12:33 EST 2018. Contains 299379 sequences. (Running on oeis4.)