This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A007527 M3793 #28 Mar 10 2025 11:46:11
%S A007527 5,10,11,20,25,26,38,39,54,65,70,114,130
%N A007527 Numbers that are not the sum of 4 hexagonal numbers.
%C A007527 The sequence is complete. "In 1830, Legendre (1979) proved that every number larger than 1791 is a sum of four hexagonal numbers". See Eric Weisstein's link and Legendre reference. It is easy to check all numbers <= 1791 by computer. - _Olivier Pirson_, Sep 14 2007
%D A007527 A.-M. Legendre, Theorie des nombres, 4th ed., 2 vols. Paris: A. Blanchard, 1979.
%D A007527 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007527 Nicholas John Bizzell-Browning, <a href="https://bura.brunel.ac.uk/handle/2438/29960">LIE scales: Composing with scales of linear intervallic expansion</a>, Ph. D. Thesis, Brunel Univ. (UK, 2024). See p. 143.
%H A007527 Shyam Sunder Gupta, <a href="https://doi.org/10.1007/978-981-97-2465-9_13">Unlucky 13</a>, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 13, 353-365.
%H A007527 R. K. Guy, <a href="http://www.jstor.org/stable/2324367">Every number is expressible as the sum of how many polygonal numbers?</a>, Amer. Math. Monthly 101 (1994), 169-172.
%H A007527 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HexagonalNumber.html">Hexagonal Number</a>
%t A007527 lim = 1791; maxa = Ceiling[a /. Last[Solve[a(2a - 1) == lim]]]; t = Flatten[ Table[a(2a - 1) + b(2b - 1) + c(2c - 1) + d(2d - 1), {a, 0, maxa}, {b, 0, a}, {c, 0, b}, {d, 0, c}], 3]; Complement[ Range[lim], t](* _Jean-François Alcover_, Sep 21 2011 *)
%K A007527 fini,nonn,full
%O A007527 1,1
%A A007527 _N. J. A. Sloane_