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).

0, 3, 5, 9, 10, 12, 5, 9, 17, 33, 33, 34, 36, 40, 48, 257, 264, 278, 288, 326, 384

Offset

1,2

Comments

Row sums are given in A230386. See A230384 for a "dual" version.

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?

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

The table reads
n=1: {0} with sum = 0,
n=2: {3,5} with sum = 8,
n=3: {9, 10, 12} with sum = 31 (the set {5, 9, 17} having the same sum but a larger maximum),
n=4: {5, 9, 17, 33} with sum = 64,
n=5: {33, 34, 36, 40, 48 } with sum = 191.
n=6: {257, 264, 278, 288, 326, 384} with sum = 1797.
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.

Crossrefs

Sequence in context: A030365 A316520 A153710 * A269399 A345916 A175468

Adjacent sequences: A230382 A230383 A230384 * A230386 A230387 A230388

Keyword

nonn,tabl,base,hard,more

Author

Vladimir Shevelev and M. F. Hasler, Oct 17 2013

Extensions

a(16)-a(21) by M. F. Hasler, Oct 18 2013

Status

approved