|
|
A327975
|
|
Breadth-first reading of the subtree rooted at 5 of the tree where each parent node is the arithmetic derivative (A003415) of all its children.
|
|
7
|
|
|
5, 6, 9, 14, 33, 49, 62, 94, 177, 817, 961, 445, 913, 1633, 2173, 2209, 1146, 886, 1822, 4414, 19193, 25829, 32393, 41033, 47429, 57929, 64133, 88229, 101753, 111173, 116729, 129413, 138233, 148553, 160229, 173093, 183929, 188453, 208613, 216773, 232229, 235913, 244229, 249929, 257573, 262793, 272633, 278153, 282533, 288329, 294473, 304613, 316229, 320933, 322853, 323429, 327653, 328313, 1155, 2649
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The branching degree of vertex v is given by A099302(v).
Leaves form a subsequence of A098700.
Most terms of A189760 (apart from 0, 1, 2, 414, ...) seem to be located in this tree, in positions where they have no smaller siblings.
For any number k at level n (where 5 is at level 2), we have A256750(k) = A327966(k) = n.
Question: Does this subtree contain infinitely long paths? How many? Cf. conjecture number 8 in Ufnarovski and Ahlander paper, and a similar tree starting from 7, A327977.
|
|
LINKS
|
|
|
EXAMPLE
|
Because we have A003415(5) = 1, A003415(6) = 5, A003415(9) = 6, A003415(14) = 9, A003415(33) = A003415(49) = 14, A003415(62) = 33, etc, this subtree is laid out as below. The terms of this sequence are obtained by scanning each successive level of the tree from left to right, from the node 5 onward:
(0)
|
(1)
|
5
|
6
|
9
|
14________________
| |
33 49
| |
62________ 94_____________________________
| | | | | | | |
| | | | | | | |
177 817 961 445 913 1633 2173 2209
| | | |
| | | |
1146 886 1822 4414
| | | |
| | | |
(19193, (1155, (19921, ..., 829921) (22045, ..., 4870849)
25829, 2649, [49 children for 4414]
..., ..., [27 children for 1822]
328313) 196249)
[19 children for 886]
[38 children
for 1146]
The row lengths thus start as: 1, 1, 1, 1, 2, 2, 8, 4, 133 (= 38+19+27+49), ...
|
|
PROG
|
(PARI)
A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
A327975list(e) = { my(lista=List([5]), f); for(n=1, e, f = lista[n]; for(k=1, 1+A002620(f), if(A003415(k)==f, listput(lista, k)))); Vec(lista); };
v328975 = A327975list(21);
'''Breadth-first reading of irregular subtree rooted at 5, defined by the edge-relation A003415(child) = parent.'''
yield 5
for k in [1 .. 1+(x*x)//2]:
def take(n, g):
'''Returns a list composed of the next n elements returned by generator g.'''
z = []
if 0 == n: return z
for x in g:
z.append(x)
if n > 1: n = n-1
else: return(z)
|
|
CROSSREFS
|
Cf. A003415, A098699, A098700, A099302, A099303, A099307, A099308, A189760, A256750, A327966, A327968, A328115.
Cf. A327977 for the subtree starting from 7, and also A263267 for another similar tree.
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|