A230384 - OEIS

%I #17 Jan 02 2023 12:30:49

%S 1,1,2,2,7,8,4,19,49,67,42,84,138,174,357,168,348,372,702,906,1407

%N 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 Row sums are given in A230387. See A230385 for a "dual" version.

%C 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 M. F. Hasler, in reply to V. Shevelev, <a href="http://list.seqfan.eu/oldermail/seqfan/2013-October/011785.html">Peculiar sets of evil numbers (Cf. A001969)</a>, SeqFan list, Oct 17 2013

%e For n=1 to 4, we have the sets

%e n=1: {1} with sum = 1,

%e n=2: {1, 2} with sum = 3

%e n=3: {2, 7, 8} with sum = 17,

%e n=4: {4, 19, 49, 67} with sum = 139.

%e 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 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 n=5: {42, 84, 138, 174, 357} with sum = 795.

%e n=6: {168, 348, 372, 702, 906, 1407} with sum = 3903.

%Y Cf. A230385, A230386.

%K nonn,base,tabl,more

%O 1,3

%A _M. F. Hasler_, Oct 17 2013

%E a(11)-a(21) from _Charles R Greathouse IV_, Oct 18 2013