login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A338260 a(n) is the number of nodes with depth of n in a binary tree defined as: root = 1 and a child (C) of a node (N) is such that A337978(C) = N. For nodes with two children, the smaller child is assigned as the left child and the bigger one as the right child. A child of a one-child node is assigned as the left child. 1
1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 3, 2, 3, 3, 3, 3, 3, 3, 4, 5, 4, 5, 4, 3, 4, 5, 6, 6, 5, 5, 4, 4, 4, 6, 6, 7, 6, 7, 7, 8, 7, 7, 6, 8, 7, 8, 8, 10, 10, 9, 8, 11, 8, 9, 9, 10, 10, 10, 11, 12, 11, 12, 13, 14, 13, 14, 14, 13, 12, 11, 13, 13, 14 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,8
COMMENTS
The binary tree, read from left to right in the order of increasing depth n, is the positive integer sequence A000027. The first 66 numbers are shown in the figure below.
1
2
3
4
5
6
7
8 \_(9)
10
11 \_12
13 14
15 16
(17) 18
19
20 \_21
22 23
24 25
(26) 27 \______28
29 30
31 \_32 (33)
34 35 \______36
37 38 39
(40) 41 42
43 44 \_45
46 47 48
(49) 50 51 \______52
53 (54)\_55 56 \______57
58 59 60 61
(62) 63 64 \_65 (66)
All right children are composite numbers and all prime numbers are left children.
a(n) in this sequence is the number of terms with value of n in A337979.
LINKS
PROG
(Python)
from sympy import primepi
def depth(k):
d = 0
while k > 1:
k += primepi(k)
k -= primepi(k)
d += 1
return d
m = 1
for n in range (0, 101):
a = 0
while depth(m + a) == n:
a += 1
print(a)
m += a
CROSSREFS
Sequence in context: A344117 A163367 A057226 * A224963 A073810 A055255
KEYWORD
nonn
AUTHOR
Ya-Ping Lu, Oct 19 2020
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 23 13:51 EDT 2024. Contains 371914 sequences. (Running on oeis4.)