%I #25 Jan 03 2025 03:00:55
%S 0,3,5,15,11,19,21,27,37,69,45,43,191,99,75,83,87,85,153,107,157,151,
%T 149,155,183,179,205,173,219,171,213,335,315,307,395,301,309,333,299,
%U 331,339,365,343,469,347,341,429,589,627,587,427,595,659,669,795,599,915,597,603,661,679,619,667,723,691,813,731,877,1181,693,685,811,1253
%N a(n) is the least k such that n is the number of halving partitions of k (=A349552(k)).
%C For m >= 1, let S(m) = {f(m/2), c(m/2)}, where f = floor and c = ceiling. A halving partition of n is a partition p(1) + p(2) + ... + p(k) = n such that p(1) is in S(n) and p(i) is in S(p(i-1)) for i = 2, 3, ..., k.
%e Let f = floor and c = ceiling.
%e a(1) = 0 corresponds to the empty halving partition of 0.
%e a(3) = 5, since 5 is the smallest number with 3 halving partitions:
%e c(5/2) + c(3/2) = 5;
%e c(5/2) + f(3/2) + c(1/2) = 3 + 1 + 1 = 5;
%e f(5/2) + (2/2) + c(1/2) + c(1/2) = 2 + 1 + 1 + 1.
%Y Cf. A349552.
%K nonn
%O 1,2
%A _Clark Kimberling_, Dec 26 2021
%E Corrected and extended by _Max Alekseyev_, Sep 30 2024