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A231632 Squares that are also sums of 2 and 3 nonzero squares. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A292559 A322568 A018820 * A202004 A020249 A287391

Adjacent sequences:  A231629 A231630 A231631 * A231633 A231634 A231635

KEYWORD

dead

AUTHOR

Zak Seidov, Nov 12 2013

STATUS

approved

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Last modified October 28 07:43 EDT 2021. Contains 348321 sequences. (Running on oeis4.)