The On-Line Encyclopedia of Integer Sequences (OEIS)

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A338409

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 A338215(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.
(history; published version)

#10 by N. J. A. Sloane at Mon Nov 23 01:45:42 EST 2020

STATUS

proposed

approved

#9 by Ya-Ping Lu at Wed Nov 04 07:54:40 EST 2020

STATUS

editing

proposed

#8 by Ya-Ping Lu at Wed Nov 04 07:49:54 EST 2020

EXAMPLE

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 \_67

STATUS

proposed

editing

Discussion

Wed Nov 04

07:54

Ya-Ping Lu: Deleted the excessive blanks on the left of the tree.

#7 by Ya-Ping Lu at Wed Nov 04 04:20:03 EST 2020

STATUS

editing

proposed

Discussion

Wed Nov 04

04:24

Hugo Pfoertner: Is there a reason for the excessive whitespace left of the tree? 2 blanks at the beginning of a line in an ASCII art diagram are sufficient to inhibit unwanted wrapping and position shifts of lines.

#6 by Ya-Ping Lu at Wed Nov 04 04:17:29 EST 2020

COMMENTS

The binary tree, read from left to right in the order of increasing depth n, is the positive integer sequence A000027. The first 67 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 \_67

All left children except 2 are composite numbers and all prime numbers are right children.

EXAMPLE

The binary tree, read from left to right in the order of increasing depth n, is the positive integer sequence A000027. The first 67 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 \_67

All left children except 2 are composite numbers and all prime numbers are right children.

STATUS

proposed

editing

Discussion

Wed Nov 04

04:19

Ya-Ping Lu: Moved the tree to example section.

#5 by Ya-Ping Lu at Tue Oct 27 11:42:59 EDT 2020

STATUS

editing

proposed

Discussion

Tue Oct 27

12:06

Michel Marcus: I wonder if the binary tree should rather go to the example section : what do other editors think ?

#4 by Ya-Ping Lu at Tue Oct 27 11:42:49 EDT 2020

COMMENTS

The binary tree, read from left to right in the order of increasing depth n, is the positive integer sequence A000027. The first ?? 67 numbers are shown in the figure below.

STATUS

proposed

editing

#3 by Ya-Ping Lu at Sat Oct 24 23:19:41 EDT 2020

STATUS

editing

proposed

#2 by Ya-Ping Lu at Sat Oct 24 23:17:33 EDT 2020

NAME

allocated for Yaa(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 A338215(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-Ping Luchild node is assigned as the left child.

DATA

1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2, 3, 4, 3, 4, 3, 4, 4, 4, 4, 6, 6, 5, 6, 4, 4, 6, 7, 7, 6, 7, 6, 5, 4, 6, 7, 8, 8, 8, 8, 10, 8, 8, 8, 9, 10, 8, 9, 11, 13, 11, 9, 12, 11, 10, 11, 11, 11, 13, 11, 14, 14, 13, 15, 17, 15, 16, 16, 16, 14, 14, 14

OFFSET

0,2

COMMENTS

The binary tree, read from left to right in the order of increasing depth n, is the positive integer sequence A000027. The first ?? 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 \_67

All left children except 2 are composite numbers and all prime numbers are right children.

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

Cf. A000027, A062298, A095117, A338215, A338237, A338260.

KEYWORD

allocated

nonn

AUTHOR

Ya-Ping Lu, Oct 24 2020

STATUS

approved

editing

#1 by Ya-Ping Lu at Sat Oct 24 23:17:33 EDT 2020

NAME

allocated for Ya-Ping Lu

KEYWORD

allocated

STATUS

approved