%I #2 Mar 30 2012 17:26:27
%S 6,10,13,22,25,32,37,43,55,61,70,79,85,91,101,113,121,129,139,145,153,
%T 163,173,187,199,205,211,217,223,243,259,269,277,289,301,309,321,331,
%U 341,353,361,373,385,391,397,411,435,451,457,463,473,481,493,509,521
%N Number of positive solutions of the Diophantine x*p+y*q=p^3+q^3, where p=nth prime, q=(n+1)th prime.
%e a(1)=6 because Diophantine 2x+3y=2^3+3^3 has 6 positive solutions {x,y}:
%e {1, 11}, {4, 9}, {7, 7}, {10, 5}, {13, 3}, {16, 1};
%e a(2)=10 because Diophantine 3x+5y=3^3+5^3 has 10 positive solutions {x, y}:
%e {4, 28}, {9, 25}, {14, 22}, {19, 19}, {24, 16}, {29, 13}, {34, 10}, {39, 7}, {44, 4}, {49, 1};
%e a(3)=13 because Diophantine 5x+7y=5^3+7^3 has 13 positive solutions {x, y}:
%e {4, 64}, {11, 59}, {18, 54}, {25, 49}, {32, 44}, {39, 39}, {46, 34}, {53, 29}, {60, 24}, {67, 19}, {74, 14}, {81, 9}, {88, 4}.
%t Table[With[{p=Prime[n],q=Prime[n+1]},Floor[q^2/p]+Floor[p^2/q]+1],{n,1,100}]
%K nonn
%O 1,1
%A _Zak Seidov_, Feb 26 2008
