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

1,3

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?

Links

Table of n, a(n) for n=1..21.

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

Example

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.

Crossrefs

Cf. A230385, A230386.

Sequence in context: A232647 A091665 A019905 * A151864 A019732 A199467

Adjacent sequences: A230381 A230382 A230383 * A230385 A230386 A230387

Keyword

nonn,base,tabl,more

Author

M. F. Hasler, Oct 17 2013

Extensions

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

Status

approved