cp's OEIS Frontend

A349553 a(n) is the least k such that n is the number of halving partitions of k (=A349552(k)).

%I A349553 #25 Jan 03 2025 03:00:55
%S A349553 0,3,5,15,11,19,21,27,37,69,45,43,191,99,75,83,87,85,153,107,157,151,
%T A349553 149,155,183,179,205,173,219,171,213,335,315,307,395,301,309,333,299,
%U A349553 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 A349553 a(n) is the least k such that n is the number of halving partitions of k (=A349552(k)).
%C A349553 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 A349553 Let f = floor and c = ceiling.
%e A349553 a(1) = 0 corresponds to the empty halving partition of 0.
%e A349553 a(3) = 5, since 5 is the smallest number with 3 halving partitions:
%e A349553   c(5/2) + c(3/2) = 5;
%e A349553   c(5/2) + f(3/2) + c(1/2) = 3 + 1 + 1 = 5;
%e A349553   f(5/2) + (2/2) + c(1/2) + c(1/2) = 2 + 1 + 1 + 1.
%Y A349553 Cf. A349552.
%K A349553 nonn
%O A349553 1,2
%A A349553 _Clark Kimberling_, Dec 26 2021
%E A349553 Corrected and extended by _Max Alekseyev_, Sep 30 2024