This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A331022 #15 Jan 12 2020 10:20:26 %S A331022 0,1,2,3,4,6,9,16,20,29,34,45 %N A331022 Numbers k such that the number of strict integer partitions of k is a power of 2. %C A331022 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. %C A331022 Conjecture: This sequence is finite. %C A331022 Conjecture: The analogous sequence for non-strict partitions is: 0, 1, 2. %C A331022 Next term > 5*10^4 if it exists. - _Seiichi Manyama_, Jan 12 2020 %e A331022 The strict integer partitions of the initial terms: %e A331022 (1) (2) (3) (4) (6) (9) %e A331022 (2,1) (3,1) (4,2) (5,4) %e A331022 (5,1) (6,3) %e A331022 (3,2,1) (7,2) %e A331022 (8,1) %e A331022 (4,3,2) %e A331022 (5,3,1) %e A331022 (6,2,1) %t A331022 Select[Range[0,1000],IntegerQ[Log[2,PartitionsQ[#]]]&] %Y A331022 The version for primes instead of powers of 2 is A035359. %Y A331022 The version for factorizations instead of strict partitions is A330977. %Y A331022 Numbers whose number of partitions is prime are A046063. %Y A331022 Cf. A000009, A000079, A001055, A036498, A045778, A318286, A330989, A330990, A330994/A330995, A330996. %K A331022 nonn,more %O A331022 0,3 %A A331022 _Gus Wiseman_, Jan 10 2020