A231632 Squares that are also sums of 2 and 3 nonzero squares.

169, 225, 289, 625, 676, 841, 900, 1156, 1225, 1369, 1521, 1681, 2025, 2500, 2601, 2704, 2809, 3025, 3364, 3600, 3721, 4225, 4624, 4900, 5329, 5476, 5625, 6084, 6724, 7225, 7569, 7921, 8100, 8281, 9025, 9409, 10000, 10201, 10404, 10816, 11025, 11236, 11881, 12100, 12321, 12769, 13225, 13456, 13689, 14161

Offset

1,1

Comments

All terms == {0, 1} (mod 4).

Intersection of A000290, A000404 and A000408.

A square n^2 is the sum of k positive squares for all 1 <= k <= n^2 - 14 iff n^2 is the sum of 2 and 3 positive squares (see A309778 and proof in Kuczma) . Consequently this is a duplicate of A018820. - Bernard Schott, Aug 17 2019

References

Marcin E. Kuczma, International Mathematical Olympiads, 1986-1999, The Mathematical Association of America, 2003, pages 76-79.

Links

Zak Seidov and Chai Wah Wu, Table of n, a(n) for n = 1..10000 n = 1..100 from Zak Seidov

Example

169 = 13^2 = 5^2 + 12^2 = 3^2 + 4^2 + 12^2;
225 = 15^2 = 9^2 + 12^2 = 2^2 + 5^2 + 14^2.

Crossrefs

Cf. A000290, A000404, A000408, A018820.

Sequence in context: A322568 A350381 A018820 * A202004 A020249 A287391

Adjacent sequences: A231629 A231630 A231631 * A231633 A231634 A231635

Keyword

dead

Author

Zak Seidov, Nov 12 2013

Status

approved