A380751 Lexicographically earliest sequence of positive integers such that for any value k, no two sets of one or more indices at which k occurs have the same sum.

1, 1, 2, 1, 2, 2, 2, 1, 3, 3, 3, 4, 3, 4, 4, 1, 2, 3, 4, 5, 5, 5, 4, 5, 6, 6, 5, 6, 7, 6, 7, 1, 5, 2, 6, 3, 7, 7, 8, 8, 6, 7, 8, 9, 8, 9, 4, 9, 9, 8, 10, 7, 10, 9, 10, 10, 8, 11, 10, 9, 11, 11, 11, 1, 10, 12, 12, 2, 11, 12, 13, 3, 12, 9, 12, 11, 10, 13, 13, 12

Offset: 1

Author

Neal Gersh Tolunsky, Jan 31 2025

Keywords

• nonn

Comments

The longest run in the sequence has length 3.

The powers of 2 (A000079) are the indices of 1s in this sequence.

Examples

			a(3) cannot be 1 since i = 1,2 would have the same sum as i = 3. So a(3) = 2.
a(12) cannot be 1 since i = 4,8 would have the same sum as i = 12. a(12) = 2 would give i = 12 the same sum as i = 5,7. a(12) = 3 would give i = 10,11 the same sum as i = 9,12. So a(12) = 4.
		

Links

• Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A380783.