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

1,3

Comments

The longest run in the sequence has length 3.

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

Links

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

Example

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.

Crossrefs

Cf. A380783.

Sequence in context: A068307 A363721 A158946 * A303428 A223853 A023645

Adjacent sequences: A380748 A380749 A380750 * A380752 A380753 A380754

Keyword

nonn

Author

Neal Gersh Tolunsky, Jan 31 2025

Status

approved