A302479 Number of partitions of n into two distinct nonprime parts.

0, 0, 0, 0, 1, 0, 1, 0, 1, 2, 1, 1, 2, 2, 2, 3, 2, 3, 3, 3, 3, 5, 3, 5, 4, 6, 4, 6, 5, 7, 6, 6, 6, 9, 6, 10, 7, 8, 8, 10, 8, 11, 9, 10, 9, 12, 9, 13, 10, 13, 10, 13, 11, 15, 12, 14, 12, 16, 13, 18, 14, 15, 14, 18, 14, 20, 15, 16, 16, 20, 16, 21, 17, 20, 17

Offset

1,10

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to partitions

Formula

a(n) = Sum_{i=1..floor((n-1)/2)} (1 - c(i)) * (1 - c(n-i)), where c = A010051.

For n > 0, a(n) = A358638(n) - A005171(n). - Antti Karttunen, Nov 25 2022

Example

a(16) = 3; 16 = 15+1 = 12+4 = 10+6, which are distinct nonprimes.

Mathematica

Table[Sum[(1 - PrimePi[n - i] + PrimePi[n - i - 1]) (1 - PrimePi[i] + PrimePi[i - 1]), {i, Floor[(n - 1)/2]}], {n, 100}]
Table[Length[Select[IntegerPartitions[n, {2}], Length[Union[#]]==2&&Boole[PrimeQ[#]]=={0, 0}&]], {n, 80}] (* Harvey P. Dale, Dec 28 2023 *)

Prog

(PARI) A302479(n) = sum(k=1, (n-1)\2, !(isprime(k)+isprime(n-k))); \\ Antti Karttunen, Nov 25 2022

Crossrefs

Cf. A005171, A010051, A062610, A358638.

Cf. also A341461, A341462, A341464, A341465, A341466, A341467.

Sequence in context: A092335 A278912 A339186 * A029355 A029307 A161066

Adjacent sequences: A302476 A302477 A302478 * A302480 A302481 A302482

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 08 2018

Status

approved