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A363069
Size of the largest subset of {1,2,...,n} such that no two elements sum to a perfect square.
0
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
1,4
FORMULA
The set: {k | k <= n, k == 1 (mod 3)} provides a lower bound: a(n) >= floor((n+2)/3).
EXAMPLE
The first few examples where a(n) increases are {1}, {1,4}, {1,4,6}, and {1,4,6,7}.
CROSSREFS
Sequence in context: A297995 A081228 A270826 * A003002 A087180 A029121
KEYWORD
nonn
AUTHOR
Zachary DeStefano, May 16 2023
STATUS
approved