A291563 Number of partitions of 2n into two prime parts or two nonprime parts.

1, 1, 1, 2, 4, 3, 4, 6, 6, 6, 8, 9, 9, 9, 11, 9, 13, 15, 10, 14, 16, 14, 16, 19, 18, 17, 21, 18, 20, 25, 18, 24, 27, 19, 26, 28, 25, 27, 32, 26, 28, 35, 29, 29, 39, 30, 32, 38, 30, 37, 41, 35, 37, 42, 38, 41, 47, 40, 40, 54, 38, 42, 53, 39, 48, 52, 46, 46

Offset

1,4

Links

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

Index entries for sequences related to partitions

Formula

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

a(n) = n - A291564(n).

Maple

a:= n-> 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[Sum[KroneckerDelta[(PrimePi[k] - PrimePi[k - 1]), (PrimePi[2 n - k] - PrimePi[2 n - 1 - k])], {k, n}], {n, 80}]

Crossrefs

Cf. A010051, A291564.

Sequence in context: A355399 A224714 A089169 * A178151 A087794 A050514

Adjacent sequences: A291560 A291561 A291562 * A291564 A291565 A291566

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 20 2017

Status

approved