A331022 Numbers k such that the number of strict integer partitions of k is a power of 2.

0, 1, 2, 3, 4, 6, 9, 16, 20, 29, 34, 45

Offset: 0

Author

Gus Wiseman, Jan 10 2020

Keywords

• nonn
• more

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

Examples

			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)
		

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.

Cf. A000009, A000079, A001055, A036498, A045778, A318286, A330989, A330990, A330994/A330995, A330996.

Programs

Mathematica

Select[Range[0,1000],IntegerQ[Log[2,PartitionsQ[#]]]&]