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%I #5 May 09 2019 15:06:22
%S 0,0,0,0,0,0,1,0,1,1,0,0,1,1,1,2,0,1,1,2,1,2,0,2,1,2,0,2,0,2,1,2,1,3,
%T 0,3,0,1,1,3,0,3,1,3,1,3,0,5,1,4,0,2,0,5,1,3,0,3,0,5,1,2,1,5,0,6,0,1,
%U 1,5,0,6,1,4,1,5,0,6,0,4,1,4,0,7,1,4
%N Number of partitions of n into 2 distinct nonadjacent prime parts.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{i=1..floor((n-1)/2)} (1-floor((pi(i)+1)/pi(n-i))) * A010051(i) * A010051(n-i), where pi is the prime counting function.
%e a(7) = 1 since 7 = 2 + 5 is the only partition of 7 into two distinct nonadjacent prime parts.
%t Table[Sum[(1 - Floor[(PrimePi[i] + 1)/PrimePi[n - i]]) (PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i] - PrimePi[n - i - 1]), {i, Floor[(n - 1)/2]}], {n, 100}]
%Y Cf. A000720, A010051.
%Y Cf. A307343.
%K nonn,easy
%O 1,16
%A _Wesley Ivan Hurt_, May 09 2019