login
A331022
Numbers k such that the number of strict integer partitions of k is a power of 2.
8
0, 1, 2, 3, 4, 6, 9, 16, 20, 29, 34, 45
OFFSET
0,3
COMMENTS
An integer partition of n is a finite, nonincreasing sequence of positive integers (parts) summing to n. It is strict if the parts are all different. Integer partitions and strict integer partitions are counted by A000041 and A000009 respectively.
Conjecture: This sequence is finite.
Conjecture: The analogous sequence for non-strict partitions is: 0, 1, 2.
Next term > 5*10^4 if it exists. - Seiichi Manyama, Jan 12 2020
EXAMPLE
The strict integer partitions of the initial terms:
(1) (2) (3) (4) (6) (9)
(2,1) (3,1) (4,2) (5,4)
(5,1) (6,3)
(3,2,1) (7,2)
(8,1)
(4,3,2)
(5,3,1)
(6,2,1)
MATHEMATICA
Select[Range[0, 1000], IntegerQ[Log[2, PartitionsQ[#]]]&]
CROSSREFS
The version for primes instead of powers of 2 is A035359.
The version for factorizations instead of strict partitions is A330977.
Numbers whose number of partitions is prime are A046063.
Sequence in context: A223900 A326020 A192267 * A256774 A213682 A103481
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jan 10 2020
STATUS
approved