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Number of ways to write n = i*p + j*q, where (p,q) is a twin prime pair and i,j>0.
0

%I #3 Mar 30 2012 18:50:38

%S 0,0,0,0,0,0,0,1,0,0,1,1,1,1,0,1,2,1,2,1,1,2,2,3,1,3,2,2,3,1,3,3,3,3,

%T 3,4,4,4,3,3,4,3,4,4,3,5,5,5,4,5,4,5,6,5,5,5,6,5,7,5,7,6,6,6,5,6,6,8,

%U 6,7,7,8,7,9,6,8,7,7,8,7,8,8,9,8,8,8,10,8,12,8,10,10,9,10,8,10,9,10,9

%N Number of ways to write n = i*p + j*q, where (p,q) is a twin prime pair and i,j>0.

%C a(A054735(n)) > 0.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimePartition.html">Prime Partition</a>

%e n=50 = 5+5+5+5+5+5+5+3+3+3+3+3 = 5+5+5+5+3+3+3+3+3+3+3+3+3+3 =

%e 5+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3 = 7+7+7+7+7+5+5+5 = 13+13+13+11, therefore

%e a(50)=5

%Y Cf. A000607, A001359, A006512.

%K nonn

%O 1,17

%A _Reinhard Zumkeller_, Aug 23 2003