A209920 Numbers n having distinct parity as the number of partitions of n.

0, 4, 6, 9, 11, 12, 14, 15, 16, 18, 19, 20, 21, 24, 25, 27, 31, 32, 36, 38, 44, 45, 47, 48, 52, 54, 55, 56, 57, 59, 60, 65, 68, 72, 75, 76, 79, 82, 88, 90, 92, 97, 101, 102, 103, 104, 109, 113, 114, 117, 118, 125, 129, 131, 132, 133, 134, 135, 137, 138, 140

Offset

1,2

Comments

Odd positive integers with an even number of partitions and nonnegative even integers with an odd number of partitions. Union of A163097 and A163096. Note that the union of A067567 and A127219 gives A194798 and the union of A194798 and this sequence gives A001477.

Links

Table of n, a(n) for n=1..61.

K. Ono, Parity of the partition function, Electronic Research Announcements of AMS, Vol. 1, 1995, pp. 35-42; MR 96d:11108

Example

4 is in the sequence because the number of partitions of 4 is equal to 5 and the parity of 4 is distinct to the parity of 5 because 4 is even and 5 is odd.
9 is in the sequence because the number of partitions of 9 is equal to 30 and the parity of 9 is distinct to the parity of 30 because 9 is odd and 30 is even.

Crossrefs

Complement of A194798.

Cf. A000041, A040051, A052001, A052003, A067567, A127219, A154795-A154798, A163096, A163097, A163998, A194807, A209658, A209659.

Sequence in context: A332618 A295329 A302990 * A258979 A258026 A246779

Adjacent sequences: A209917 A209918 A209919 * A209921 A209922 A209923

Keyword

nonn

Author

Omar E. Pol, Mar 16 2012

Status

approved