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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.

%I A338260 #7 Oct 21 2020 22:52:31
%S A338260 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,
%T A338260 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,
%U A338260 11,12,11,12,13,14,13,14,14,13,12,11,13,13,14
%N 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.
%C A338260 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.
%C A338260                          1
%C A338260                         2
%C A338260                        3
%C A338260                       4
%C A338260                      5
%C A338260                     6
%C A338260                    7
%C A338260                   8 \_(9)
%C A338260                 10
%C A338260                11 \_12
%C A338260               13   14
%C A338260              15   16
%C A338260            (17)  18
%C A338260                 19
%C A338260                20 \_21
%C A338260               22   23
%C A338260              24   25
%C A338260            (26)  27 \______28
%C A338260                 29        30
%C A338260                31 \_32  (33)
%C A338260               34   35 \______36
%C A338260              37   38        39
%C A338260            (40)  41        42
%C A338260                 43        44 \_45
%C A338260                46        47   48
%C A338260              (49)       50   51 \______52
%C A338260                        53  (54)\_55   56 \______57
%C A338260                       58        59   60        61
%C A338260                     (62)       63   64 \_65  (66)
%C A338260 All right children are composite numbers and all prime numbers are left children.
%C A338260 a(n) in this sequence is the number of terms with value of n in A337979.
%o A338260 (Python)
%o A338260 from sympy import primepi
%o A338260 def depth(k):
%o A338260     d = 0
%o A338260     while k > 1:
%o A338260         k += primepi(k)
%o A338260         k -= primepi(k)
%o A338260         d += 1
%o A338260     return d
%o A338260 m = 1
%o A338260 for n in range (0, 101):
%o A338260     a = 0
%o A338260     while depth(m + a) == n:
%o A338260         a += 1
%o A338260     print(a)
%o A338260     m += a
%Y A338260 Cf. A000027, A062298, A095117, A337978, A337979.
%K A338260 nonn
%O A338260 0,8
%A A338260 _Ya-Ping Lu_, Oct 19 2020