A363069 Size of the largest subset of {1,2,...,n} such that no two elements sum to a perfect square.

1, 1, 1, 2, 2, 3, 4, 4, 4, 4, 5, 5, 6, 6, 6, 7, 8, 8, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 26, 27, 27

Offset: 1

Author

Zachary DeStefano, May 16 2023

Keywords

• nonn

Examples

			The first few examples where a(n) increases are {1}, {1,4}, {1,4,6}, and {1,4,6,7}.
		

Links

• Z. DeStefano, Maximum Sized Sets With Sums That Avoid Squares

Crossrefs

Cf. A100719, A210380.

Formula

The set: {k | k <= n, k == 1 (mod 3)} provides a lower bound: a(n) >= floor((n+2)/3).