A291563 - OEIS

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

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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