A343267 Numbers that are not the sum of four or fewer terms from A020330 (not necessarily distinct).

1, 2, 4, 5, 7, 8, 11, 14, 17, 22, 27, 29, 32, 34, 37, 41, 44, 47, 53, 62, 95, 104, 107, 113, 116, 122, 125, 131, 134, 140, 143, 148, 155, 158, 160, 167, 407, 424, 441, 458, 475, 492, 509, 526, 552, 560, 569, 587, 599, 608, 613, 620, 638, 653, 671, 686

Offset: 1

Author

Amiram Eldar, Apr 09 2021

Keywords

• nonn
• fini
• full

Comments

Madhusudan et al. (2018) proved that a(56) = 686 is the last term of this sequence.

Links

• Parthasarathy Madhusudan, Dirk Nowotka, Aayush Rajasekaran and Jeffrey Shallit, Lagrange's Theorem for Binary Squares, in: I. Potapov, P. Spirakis and J. Worrell (eds.), 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018), Schloss Dagstuhl, 2018, pp. 18:1-18:14; arXiv preprint, arXiv:1710.04247 [math.NT], 2017-2018.

Crossrefs

Cf. A020330, A290334, A290335, A298731, A343268.

Programs

Mathematica

v = Table[n + n * 2^Floor[Log2[n] + 1], {n, 0, 20}]; Complement[Range[0, 700], Plus @@@ Tuples[v, 4]]