OFFSET
1,1
COMMENTS
Permutation of A328117.
The branching degree of vertex v is given by A099302(v).
Leaves form a subsequence of A098700.
Question: Does this subtree contain infinitely long paths? How many? Cf. conjecture number 8 in Ufnarovski and Ahlander paper. As an example of possible beginning of such a sequence they give: 1 ← 7 ← 10 ← 25 ← 46 ← 129 ← 170 ← 501 ← 414 ← 2045.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..204
Victor Ufnarovski and Bo Ahlander, How to Differentiate a Number, J. Integer Seqs., Vol. 6, 2003.
EXAMPLE
The 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 7 onward:
(0)
|
(1)
|
7
|
10______________________________
| |
21________ 25
| | |
18___ 38_____ 46_________________________________
| | | | | | | |
65 77 217 361____ 129____ 205 493_____ 529
| | | | | | |
98 426 718 170 254 462 982
| | | | | | |
[3] [21] [15] [9] [9] [28] [17]
PROG
(PARI)
A002620(n) = ((n^2)>>2);
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
A327977list(e) = { my(lista=List([7]), f); for(i=1, e, f = lista[i]; for(k=1, 1+A002620(f), if(A003415(k)==f, listput(lista, k)))); Vec(lista); };
(PARI)
\\ With precomputed large A328117, use this:
v328117 = readvec("a328117.txt");
A327977list(e) = { my(lista=List([7]), f, i); for(n=1, e, f = lista[n]; print("n=", n, " #lista=", #lista, " A002620(", f, ")=", A002620(f)); my(u=1+A002620(f)); if(u>=v328117[#v328117], print("Not enough precomputed terms of A328117 as search upper limit ", u, " > ", v328117[#v328117], " (the last item in v328117). Number of expansions so far=", n); return(1/0)); i=1; while(v328117[i]<u, if(A003415(v328117[i])==f, listput(lista, v328117[i])); i++)); Vec(lista); };
v327977 = A327977list(114);
A327977(n) = v327977[n];
for(n=1, #v327977, write("b327977.txt", n, " ", A327977(n)));
(Sage) # uses[A003415]
def A327977():
'''Breadth-first reading of irregular subtree rooted at 7, defined by the edge-relation A003415(child) = parent. Starts giving terms from 7 onward, after a(0) = 0 and a(1) = 1.'''
yield 7
for x in A327977():
for k in [1 .. 1+floor((x*x)/2)]:
if(A003415(k) == x): yield k
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)
take(52, A327977())
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Antti Karttunen, Oct 02 2019
STATUS
approved