A227065 The number of partitions of 2n into exactly two parts such that the smaller and larger parts are not both prime.

1, 1, 2, 3, 3, 5, 5, 6, 7, 8, 8, 9, 10, 12, 12, 14, 13, 14, 17, 17, 17, 19, 19, 19, 21, 23, 22, 25, 25, 24, 28, 27, 27, 32, 30, 30, 32, 33, 32, 36, 36, 34, 38, 40, 36, 42, 42, 41, 46, 44, 43, 47, 47, 46, 49, 49, 47, 52, 53, 48, 57, 57, 53, 61, 58, 57, 61, 63, 61, 63

Offset

1,3

Comments

Complement of A045917(n).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Index entries for sequences related to partitions

Formula

a(n) = n - A045917(n).

Maple

A227065 := proc(n)
    n-A045917(n) ;
end proc:
seq(A227065(n), n=1..100) ; # R. J. Mathar, Jul 01 2013

Mathematica

Table[n - Sum[(PrimePi[2 n - i] - PrimePi[2 n - i - 1]) (PrimePi[i] - PrimePi[i - 1]), {i, n}], {n, 100}] (* Wesley Ivan Hurt, Apr 07 2018 *)
f[n_]:=Length[Select[2 n - Prime[Range[PrimePi[n]]], PrimeQ]]; Table[n - f[n], {n, 100}] (* Vincenzo Librandi, Apr 10 2018 *)

Crossrefs

Cf. A045917.

Sequence in context: A353714 A159237 A335599 * A010761 A320840 A161172

Adjacent sequences: A227062 A227063 A227064 * A227066 A227067 A227068

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jun 30 2013

Status

approved