A309228 a(n) is the greatest possible height of a binary tree where all nodes hold positive squares and all interior nodes also equal the sum of their two children and the root node has value n^2.
1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 3, 1, 2, 1, 3, 1, 1, 2, 1, 1, 1, 1, 3, 3, 1, 1, 3, 2, 1, 1, 1, 3, 2, 1, 3, 1, 3, 2, 3, 1, 1, 1, 2, 1, 1, 1, 1, 3, 3, 3, 3, 1, 2, 1, 1, 3, 1, 2, 3, 1, 1, 1, 4, 1, 1, 3, 1, 2, 1, 1, 3, 3, 3, 1, 1, 3, 1, 2, 1, 3, 1, 1, 4, 1, 3
Offset: 1
Keywords
Examples
a(1) = 1:
1^2
|
a(5) = 2:
3^2 4^2
\ /
\ /
5^2
|
a(13) = 3:
3^2 4^2
\ /
\ /
5^2 12^2
\ /
\ /
13^2
|
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
-
Maple
f:= proc(n) option remember; local S,x,y; S:= map(t -> subs(t,[x,y]), {isolve(x^2+y^2=n^2)}); S:= select(t -> type(t,list(posint)) and t[2]>=t[1], S); if S = {} then 1 else 1+max(map(procname,map(op,S))) fi end proc: map(f, [$1..100]); # Robert Israel, Feb 27 2022 -
Mathematica
a = Table[1, {m = 100}]; Do[Do[If[IntegerQ@ Sqrt[v2 = n^2-u^2], a[[n]] = Max[a[[n]], 1+Max[a[[u]], a[[Floor@ Sqrt[v2]]]]]], {u, 1, n-1}], {n, 1, m}]; Table[a[[n]], {n, 1, m}] (* Jean-François Alcover, Aug 19 2022, after PARI code *) -
PARI
a = vector(87,n,1); for (n=1, #a, for (u=1, n-1, if (issquare(v2=n^2-u^2), a[n]=max(a[n],1+max(a[u],a[sqrtint(v2)])))); print1 (a[n]", "))
Comments