cp's OEIS Frontend

A230385 Table read by rows: Least set of n evil numbers (A001969) such that any two or more add up to an odious number (A000069); ordered by total sum of the elements, then by the size of the largest element(s).

%I A230385 #13 Dec 23 2024 14:53:43
%S A230385 0,3,5,9,10,12,5,9,17,33,33,34,36,40,48,257,264,278,288,326,384
%N A230385 Table read by rows: Least set of n evil numbers (A001969) such that any two or more add up to an odious number (A000069); ordered by total sum of the elements, then by the size of the largest element(s).
%C A230385 Row sums are given in A230386. See A230384 for a "dual" version.
%C A230385 Is this sequence finite, or is there for any n at least one admissible set of n evil numbers, i.e., such that any sum of two or more elements add up to an odious number?
%H A230385 M. F. Hasler, in reply to V. Shevelev, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2013-October/011785.html">Peculiar sets of evil numbers (Cf. A001969)</a>, SeqFan list, Oct 17 2013
%e A230385 The table reads
%e A230385 n=1: {0} with sum = 0,
%e A230385 n=2: {3,5} with sum = 8,
%e A230385 n=3: {9, 10, 12} with sum = 31 (the set {5, 9, 17} having the same sum but a larger maximum),
%e A230385 n=4: {5, 9, 17, 33} with sum = 64,
%e A230385 n=5: {33, 34, 36, 40, 48 } with sum = 191.
%e A230385 n=6: {257, 264, 278, 288, 326, 384} with sum = 1797.
%e A230385 For example, for n=4, all 11 numbers 5+9=14,5+17=22,5+33=38,9+17=26, 9+33=42, 17+33=50, 5+9+17=31, 5+9+33=47, 5+17+33=55, 9+17+33=59, 5+9+17+33=64 are odious.
%K A230385 nonn,tabl,base,hard,more
%O A230385 1,2
%A A230385 _Vladimir Shevelev_ and _M. F. Hasler_, Oct 17 2013
%E A230385 a(16)-a(21) by _M. F. Hasler_, Oct 18 2013