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

0, 3, 5, 15, 11, 19, 21, 27, 37, 69, 45, 43, 191, 99, 75, 83, 87, 85, 153, 107, 157, 151, 149, 155, 183, 179, 205, 173, 219, 171, 213, 335, 315, 307, 395, 301, 309, 333, 299, 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

Offset: 1

Author

Clark Kimberling, Dec 26 2021

Keywords

• nonn

Comments

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.

Examples

			Let f = floor and c = ceiling.
a(1) = 0 corresponds to the empty halving partition of 0.
a(3) = 5, since 5 is the smallest number with 3 halving partitions:
  c(5/2) + c(3/2) = 5;
  c(5/2) + f(3/2) + c(1/2) = 3 + 1 + 1 = 5;
  f(5/2) + (2/2) + c(1/2) + c(1/2) = 2 + 1 + 1 + 1.
		

Crossrefs

Cf. A349552.

Extensions

Corrected and extended by Max Alekseyev, Sep 30 2024