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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. 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 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

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