A290334 Numbers that are not the sum of three or fewer terms from A020330.

1, 2, 4, 5, 7, 8, 11, 12, 14, 17, 19, 22, 24, 26, 27, 29, 31, 32, 34, 37, 38, 41, 43, 44, 47, 50, 52, 53, 59, 62, 68, 71, 77, 80, 85, 86, 89, 92, 94, 95, 97, 98, 101, 103, 104, 106, 107, 110, 112, 113, 115, 116, 119, 121, 122, 124, 125, 128, 130, 131, 133, 134, 137, 138, 140, 143, 145, 147, 148, 150, 152, 155, 157, 158, 160, 164, 165

Offset

1,2

Comments

Not currently proved that there are infinitely many terms. It is conjectured that all integers > 686 are the sum of four binary squares.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Aayush Rajasekaran, Jeffrey Shallit and Tim Smith, Sums of Palindromes: an Approach via Nested-Word Automata, in: Rolf Niedermeier and Brigitte Vallée, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018), Schloss Dagstuhl, 2018, pp. 54:1-54:12; arXiv preprint, arXiv:1706.10206 [cs.FL], June 30 2017.

Mathematica

v = Table[n + n * 2^Floor[Log2[n] + 1], {n, 0, 12}]; Complement[Range[v[[-1]]], Plus @@@ Tuples[v, 3]] (* Amiram Eldar, Apr 09 2021 *)

Crossrefs

Cf. A020330, A290335, A298731.

Sequence in context: A188298 A289129 A368364 * A206285 A356449 A229303

Adjacent sequences: A290331 A290332 A290333 * A290335 A290336 A290337

Keyword

nonn

Author

Jeffrey Shallit, Jul 27 2017

Status

approved