OFFSET
4,1
COMMENTS
Nodes with degree > 2 that have the greatest number of vertices in prime XOR connected graphs are defined as maximal nodes. The graph is constructed in the manner outlined in A200143.
EXAMPLE
The XOR connected graph for the interval [33,63], n=5, is
37 41 43 47 53 59 61
37 0 0 1 0 0 1 0
41 0 0 1 1 0 0 0 37
43 1 1 0 0 1 0 0 / \
47 0 1 0 0 0 0 0 or 47~41~43 59~61
53 0 0 1 0 0 1 0 \ /
59 1 0 0 0 1 0 1 53
61 0 0 0 0 0 1 0
The maximum number of vertices connected to any prime is 3, therefore 43 and 59 are members of row n=5.
Triangle begins:
17;
43, 59;
103;
139, 151, 157, 173, 193;
281, 457, 461, 463, 499;
607;
1409, 1451;
MAPLE
q:= (l, p, r)-> `if`(r-l=2, 0, `if`(isprime(l+r-p), 1, 0)+
`if`((l+r)/2>p, q(l, p, (l+r)/2), q((l+r)/2, p, r))):
T:= proc(n) local r, l, u, p, m, d;
r:= NULL;
l:= 2^n; u:= 2*l;
p:= nextprime(l);
m:= -1;
while p<=u do
d:= q(l, p, u);
if d=m then r:= r, p
elif d>m then m:= d; r:= p fi;
p:= nextprime(p)
od;
`if`(m>=3, r, NULL)
end:
seq(T(n), n=4..18); # Alois P. Heinz, Nov 16 2011
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Brad Clardy, Nov 15 2011
EXTENSIONS
More terms from Alois P. Heinz, Nov 16 2011
STATUS
approved