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A230384 Table read by rows: Least set of n odious numbers (A000069) such that any two or more add to an evil number (A001969); ordered by total sum of elements, then by largest element(s).

%I A230384 #18 Dec 23 2024 14:53:43
%S A230384 1,1,2,2,7,8,4,19,49,67,42,84,138,174,357,168,348,372,702,906,1407
%N A230384 Table read by rows: Least set of n odious numbers (A000069) such that any two or more add to an evil number (A001969); ordered by total sum of elements, then by largest element(s).
%C A230384 Row sums are given in A230387. See A230385 for a "dual" version.
%C A230384 Is this sequence finite, or is there for any n at least one admissible set of n odious numbers, i.e., such that any sum of two or more elements add up to an evil number?
%H A230384 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 A230384 For n=1 to 4, we have the sets
%e A230384 n=1: {1} with sum = 1,
%e A230384 n=2: {1, 2} with sum = 3
%e A230384 n=3: {2, 7, 8} with sum = 17,
%e A230384 n=4: {4, 19, 49, 67} with sum = 139.
%e A230384 E.g., for n=3, the numbers 2, 7 and 8 have an odd bit sum, but 2+7, 2+8, 7+8 and 2+7+8 all have an odd bit sum.
%e A230384 For n=4, we also have the admissible set {14, 31, 44, 61} which has a smaller maximal element, but a larger total sum.
%e A230384 n=5: {42, 84, 138, 174, 357} with sum = 795.
%e A230384 n=6: {168, 348, 372, 702, 906, 1407} with sum = 3903.
%Y A230384 Cf. A230385, A230386.
%K A230384 nonn,base,tabl,more
%O A230384 1,3
%A A230384 _M. F. Hasler_, Oct 17 2013
%E A230384 a(11)-a(21) from _Charles R Greathouse IV_, Oct 18 2013