A291564 - OEIS

%I #21 Mar 05 2021 16:43:56

%S 0,1,2,2,1,3,3,2,3,4,3,3,4,5,4,7,4,3,9,6,5,8,7,5,7,9,6,10,9,5,13,8,6,

%T 15,9,8,12,11,7,14,13,7,14,15,6,16,15,10,19,13,10,17,16,12,17,15,10,

%U 18,19,6,23,20,10,25,17,14,21,22,17,20,19,12,23,24

%N Number of partitions of 2n into two parts such that one part is prime and the other is nonprime.

%H Alois P. Heinz, <a href="/A291564/b291564.txt">Table of n, a(n) for n = 1..20000</a>

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) = n - Sum_{i=1..n} [A010051(i) = A010051(2n-i)], where [] is the Iverson bracket.

%F a(n) = n - A291563(n).

%p a:= n-> add(`if`(isprime(n+i) xor isprime(n-i), 1, 0), i=1..n-1):

%p seq(a(n), n=1..80);  # _Alois P. Heinz_, Mar 05 2021

%t Table[n - Sum[KroneckerDelta[(PrimePi[k] - PrimePi[k - 1]), (PrimePi[2 n - k] - PrimePi[2 n - 1 - k])], {k, n}], {n, 80}]

%Y Cf. A010051, A291563.

%K nonn,look,easy

%O 1,3

%A _Wesley Ivan Hurt_, Oct 20 2017