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).

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

Offset: 1

Author

M. F. Hasler, Oct 17 2013

Keywords

• nonn
• base
• tabl
• more

Comments

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

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?

Examples

			For n=1 to 4, we have the sets
n=1: {1} with sum = 1,
n=2: {1, 2} with sum = 3
n=3: {2, 7, 8} with sum = 17,
n=4: {4, 19, 49, 67} with sum = 139.
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.
For n=4, we also have the admissible set {14, 31, 44, 61} which has a smaller maximal element, but a larger total sum.
n=5: {42, 84, 138, 174, 357} with sum = 795.
n=6: {168, 348, 372, 702, 906, 1407} with sum = 3903.
		

Links

• M. F. Hasler, in reply to V. Shevelev, Peculiar sets of evil numbers (Cf. A001969), SeqFan list, Oct 17 2013

Crossrefs

Cf. A230385, A230386.

Extensions

a(11)-a(21) from Charles R Greathouse IV, Oct 18 2013