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A346958 a(n) is the minimal number of cubes required to make a void of volume n.

%I A346958 #22 Sep 23 2022 11:55:39
%S A346958 6,10,13,15,17,18,18,21,23,25,26,26
%N A346958 a(n) is the minimal number of cubes required to make a void of volume n.
%C A346958 Following is an illustration of the first few voids in the form of polycubes (where an o represents a continuation upwards and an x represents a continuation downwards) each of which can be made by concealing it with a(n) cubes.
%C A346958                           .---.       .---.
%C A346958                           |   |       |   |
%C A346958   .---.   .---.---.   .---.---.   .---.---.
%C A346958   |   |   |   |   |   |   |   |   |   | o |
%C A346958   .---.   .---.---.   .---.---.   .---.---.
%C A346958    n=1       n=2         n=3         n=4
%C A346958       .---.       .---.           .---.
%C A346958       |   |       |   |           |   |
%C A346958   .---.---.   .---.---.---.   .---.---.---.
%C A346958   |   | o |   |   | o |   |   |   | ox|   |
%C A346958   .---.---.   .---.---.---.   .---.---.---.
%C A346958       |   |       |   |           |   |
%C A346958       .---.       .---.           .---.
%C A346958      n=5           n=6             n=7
%C A346958 Equivalently, the minimum perimeter size of any polycube of size n. - _Sean A. Irvine_, Aug 23 2021
%C A346958 Conjecture: When n is in A001845 the void is an octahedral crystal ball of volume n = A001845(m), which is concealed by a(n) = A005899(m+1) cubes. So a(A001845(m)) = A005899(m+1), m>=0. For example, a(1)=6 and a(7)=18. - _Mohammed Yaseen_, Sep 15 2022
%H A346958 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a346/A346958.java">Java program</a> (github)
%F A346958 a(n) < A193416(n) for n>2.
%e A346958 A cube-shaped void can be made by concealing it with 6 cubes, which is the minimal number to do so. So a(1)=6.
%e A346958 A dicube-shaped void can be made by concealing it with 10 cubes, which is the minimal number to do so. So a(2)=10.
%Y A346958 Cf. A261491 (2D analog).
%Y A346958 Cf. A000162, A003211, A193416.
%K A346958 nonn,hard,more
%O A346958 1,1
%A A346958 _Mohammed Yaseen_, Aug 08 2021
%E A346958 a(8)-a(12) from _Sean A. Irvine_, Aug 23 2021