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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.

%I A200321 #15 Nov 14 2014 10:42:19
%S A200321 17,43,59,103,139,151,157,173,193,281,457,461,463,499,607,1409,1451,
%T A200321 2143,2657,4229,16063,19583,19699,62143,124981,166303,172663,240257,
%U A200321 244301,276041,289853,305411,327319,376639,417941,505663,518761,524119,600703,1056287
%N 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.
%C A200321 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.
%e A200321 The XOR connected graph for the interval [33,63], n=5, is
%e A200321    37 41 43 47 53 59 61
%e A200321 37  0  0  1  0  0  1  0
%e A200321 41  0  0  1  1  0  0  0             37
%e A200321 43  1  1  0  0  1  0  0            /  \
%e A200321 47  0  1  0  0  0  0  0 or 47~41~43   59~61
%e A200321 53  0  0  1  0  0  1  0            \  /
%e A200321 59  1  0  0  0  1  0  1             53
%e A200321 61  0  0  0  0  0  1  0
%e A200321 The maximum number of vertices connected to any prime is 3, therefore 43 and 59 are members of row n=5.
%e A200321 Triangle begins:
%e A200321 17;
%e A200321 43,   59;
%e A200321 103;
%e A200321 139,  151,  157,  173,  193;
%e A200321 281,  457,  461,  463,  499;
%e A200321 607;
%e A200321 1409, 1451;
%p A200321 q:= (l, p, r)-> `if`(r-l=2, 0, `if`(isprime(l+r-p), 1, 0)+
%p A200321                 `if`((l+r)/2>p, q(l, p, (l+r)/2), q((l+r)/2, p, r))):
%p A200321 T:= proc(n) local r, l, u, p, m, d;
%p A200321       r:= NULL;
%p A200321       l:= 2^n; u:= 2*l;
%p A200321       p:= nextprime(l);
%p A200321       m:= -1;
%p A200321       while p<=u do
%p A200321         d:= q(l, p, u);
%p A200321         if d=m then r:= r,p
%p A200321       elif d>m then m:= d; r:= p fi;
%p A200321         p:= nextprime(p)
%p A200321       od;
%p A200321       `if`(m>=3, r, NULL)
%p A200321     end:
%p A200321 seq(T(n), n=4..18);  # _Alois P. Heinz_, Nov 16 2011
%Y A200321 Cf. A200143.
%K A200321 nonn,tabf
%O A200321 4,1
%A A200321 _Brad Clardy_, Nov 15 2011
%E A200321 More terms from _Alois P. Heinz_, Nov 16 2011