A291564 Number of partitions of 2n into two parts such that one part is prime and the other is nonprime.

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, 15, 9, 8, 12, 11, 7, 14, 13, 7, 14, 15, 6, 16, 15, 10, 19, 13, 10, 17, 16, 12, 17, 15, 10, 18, 19, 6, 23, 20, 10, 25, 17, 14, 21, 22, 17, 20, 19, 12, 23, 24

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Index entries for sequences related to partitions

Formula

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

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

Maple

a:= n-> add(`if`(isprime(n+i) xor isprime(n-i), 1, 0), i=1..n-1):
seq(a(n), n=1..80);  # Alois P. Heinz, Mar 05 2021

Mathematica

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

Crossrefs

Cf. A010051, A291563.

Sequence in context: A254044 A274515 A362500 * A029266 A325035 A348331

Adjacent sequences: A291561 A291562 A291563 * A291565 A291566 A291567

Keyword

nonn,look,easy

Author

Wesley Ivan Hurt, Oct 20 2017

Status

approved