A377084 a(n) is the maximum integer for which some minimum-length sum equaling a(n) of perfect squares less than n^2 excludes (n-1)^2.

3, 16, 31, 128, 191, 324, 368, 561, 891, 1200, 1104, 1993, 2535, 2692, 2896, 4321, 4880, 5832, 5776, 7485, 9144, 9680, 8903, 14353, 15576, 14872, 14527, 22736, 21697, 22500, 22587, 30537, 31451, 33524, 30076, 42768, 43664, 43097, 39317, 59200, 58835, 59893

Offset: 3

Author

N. Bradley Fox, Nathan Fox, Helen Grundman, Rachel Lynn, Changningphaabi Namoijam, Mary Vanderschoot, Oct 15 2024

Keywords

• nonn

Examples

			561 cannot be written as a sum of fewer than nine perfect squares less than 10^2. 561 can be written as a sum of nine of these numbers in five ways:
561 = 1^2 + 5^2 + 7^2 + 9^2 + 9^2 + 9^2 + 9^2 + 9^2 + 9^2
561 = 3^2 + 6^2 + 8^2 + 8^2 + 8^2 + 9^2 + 9^2 + 9^2 + 9^2
561 = 3^2 + 7^2 + 7^2 + 7^2 + 9^2 + 9^2 + 9^2 + 9^2 + 9^2
561 = 5^2 + 5^2 + 5^2 + 9^2 + 9^2 + 9^2 + 9^2 + 9^2 + 9^2
561 = 7^2 + 8^2 + 8^2 + 8^2 + 8^2 + 8^2 + 8^2 + 8^2 + 8^2
The last sum here does not include 9^2, so a(10) >= 561. In fact, a(10) = 561, as every number larger than 561 has 9^2 in every shortest decomposition of this form.
		

Links

• Nathan Fox, Table of n, a(n) for n = 3..100
• N. Bradley Fox et al., Elated Numbers, arXiv:2409.09863 [math.NT], 2024.

Crossrefs

Cf. A377085.