

A165565


a(n) = na(a(a(n3))) with a(0)=a(1)=a(2)=0.


0



0, 0, 0, 3, 4, 5, 3, 3, 3, 6, 7, 8, 9, 10, 11, 12, 13, 14, 12, 12, 12, 15, 16, 17, 15, 15, 15, 18, 19, 20, 21, 22, 23, 21, 21, 21, 24, 25, 26, 27, 28, 29, 30, 31, 32, 30, 30, 30, 33, 34, 35, 36, 37, 38, 39, 40, 41, 39, 39, 39, 42, 43, 44, 42, 42, 42, 45, 46, 47, 48, 49, 50, 51, 52
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


COMMENTS

A generalization of the Hofstadter Gsequence A005206 since it is part of the following family of sequences (which would give for k=1, p=2 the original Gsequence):
a(n)=n(a^p)(nk) where (a^p) denotes p recurrences of a on the given argument (e.g. this sequence would be denoted as n(a^3)(n3)) with a(0)=a(1)=...=a(k1)=0 with k=1,2,3..., p=1,2,3... (here k=p=3)
Shares nearly all properties with the a(n)=n(a(a(nk)) family (quote from the page of the k=2Sequence of this family, A163873, which applies to this family as well):
"Some things can be said about this family of sequences: Every a(n) occurs either exactly one or exactly k+1 times (except from the initial values which occur k times). A block of k+1 occurences of the same number n is after the first one interrupted by the following k1 elements: n+1, n+2, ..., n+k1 (e.g. see from [for this sequence: a(15) to a(20): 12,13,14,12,12,12]).
Since every natural number occurs in each sequence of the family at least once and 0<=a(n)<=n for all n [to be precisely: From the (2*k)th element on] the elements can be ordered in such a way that every n is connected to its a(n) in a tree structure so that:
.a(n)
....
..a.."
This will give a (k+1)ary tree which (Conjecture:) features a certain structure (similar to the Gsequence A005206 or other sequences of the above mentioned family:
A163873, A163875 and A163874). If the (below) following two constructs (C and D) are added on top of their ends (either marked with C or D) one will (if starting with one instance of D) receive the above tree (x marks a node, o marks spaces for nodes that are not part of the construct but will be filled by the other construct, constructs apply only to this sequence, comments for the whole family!):
Diagram of D:
......x..........
..../...\\\......
.../.....\\.\....
../.......\.\.\..
.D...o.o...x.x.x.
..............
...........x.x.x.
..............
...........D.C.C.
(o will be filled by C)
Diagram of C:
\\...x.
\\\./..
.\\/...
../\\..
./.\\\.
C...\\\
(This means construct C crosses on its way from a(n) to n exactly k other paths, e.g. from 14 to 17)
The first node of D has always k+1 children nodes where the first one consists of a new copy of D, the second one consists of (p1) other nodes and then D. The remaining children nodes consist of (p1) other nodes and then C. Between the first and the second leaf is always space for k1 nodes of construct C. Construct C crosses on its way from a(n) to n always exactly k paths (the right ones from construct D).


LINKS

Table of n, a(n) for n=0..73.


CROSSREFS

Mix from Hofstader HSequence A005374 and the MetaHofstadter G(3)Sequence A163874.
Sequence in context: A016553 A228947 A163874 * A033706 A121890 A178231
Adjacent sequences: A165562 A165563 A165564 * A165566 A165567 A165568


KEYWORD

easy,nonn


AUTHOR

Daniel Platt (d.platt(AT)web.de), Sep 22 2009


STATUS

approved



