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A200321
Irregular triangle T(n,k) where row n contains the maximal nodes in the graph of XOR connected primes of interval [2^n+1,2^(n+1)-1], n>=4.
1
17, 43, 59, 103, 139, 151, 157, 173, 193, 281, 457, 461, 463, 499, 607, 1409, 1451, 2143, 2657, 4229, 16063, 19583, 19699, 62143, 124981, 166303, 172663, 240257, 244301, 276041, 289853, 305411, 327319, 376639, 417941, 505663, 518761, 524119, 600703, 1056287
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
Cf. A200143.
Sequence in context: A123592 A260553 A165285 * A165981 A109998 A328998
KEYWORD
nonn,tabf
AUTHOR
Brad Clardy, Nov 15 2011
EXTENSIONS
More terms from Alois P. Heinz, Nov 16 2011
STATUS
approved