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, 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

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

Table of n, a(n) for n=0..79.

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, A337978, A337979.

Sequence in context: A344117 A163367 A057226 * A224963 A073810 A055255

Adjacent sequences: A338257 A338258 A338259 * A338261 A338262 A338263

Keyword

nonn

Author

Ya-Ping Lu, Oct 19 2020

Status

approved