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 A045914 #49 Apr 22 2025 02:42:21
%S A045914 0,1,3,6,55,66,666
%N A045914 Triangular numbers with all digits the same.
%C A045914 Escott (1905) proved that there are no more terms with fewer than 30 digits. The complete proof that there are no more terms was given by Ballew and Weger (1972). - _Amiram Eldar_, Jan 22 2022
%C A045914 Hercher and Fegert pointed out that the proof by Ballew and Weger was flawed, and provided an alternative proof (2025). - _Seiichi Azuma_, Mar 25 2025
%D A045914 L. E. Dickson, History of the Theory of Numbers, Vol. II, p. 33, Chelsea NY, 1952.
%D A045914 E. B. Escott, Math. Quest. Educational Times, New Series, Vol. 8 (1905), pp. 33-34. - _N. J. A. Sloane_, Mar 31 2014
%H A045914 David W. Ballew and Ronald C. Weger, <a href="https://web.archive.org/web/20200720220508/https://sdaos.org/wp-content/uploads/pdfs/Vol%2051%201972/72p52.pdf">Triangular Numbers with Repeated Digits</a>, Proc. S. D. Acad. Sci., Vol. 51 (1972), pp. 52-55.
%H A045914 David W. Ballew and Ronald C. Weger, <a href="https://yutaka-nishiyama.sakura.ne.jp/math/repdigit.pdf">Repdigit triangular numbers</a>, J. Rec. Math., Vol. 8, No. 2 (1975-76), pp. 96-98.
%H A045914 Christian Hercher and Karl Fegert, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL28/Hercher/hercher33.html">Triangular Numbers With a Single Repeated Digit</a>, Journal of Integer Sequences, Vol. 28 (2025), Article 25.2.1.
%H A045914 Bir Kafle, Florian Luca and Alain Togbé, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Abstracts/56-4/kafle.pdf">Triangular Repblocks</a>, Fibonacci Quart., Vol. 56, No. 4 (2018), pp. 325-328.
%H A045914 C. E. Youngman, <a href="https://archive.org/details/educationaltimes58educ/page/87/mode/1up">Problem 15648</a>, Educational Times, Vol. 58, 1905, p. 87; with a solution by E. B. Escott.
%F A045914 A118668(a(n)) = 1. - _Reinhard Zumkeller_, Jul 11 2015
%t A045914 Select[Union[Flatten[Table[FromDigits[PadRight[{},n,k]],{n,3},{k,0,9}]]],OddQ[ Sqrt[8#+1]]&] (* _Harvey P. Dale_, Feb 11 2020 *)
%Y A045914 Cf. A213516 (triangular numbers having only 1 or 2 different digits).
%Y A045914 Cf. A118668.
%K A045914 fini,full,nonn,base
%O A045914 1,3
%A A045914 _Felice Russo_
%E A045914 0 inserted by _T. D. Noe_, Jun 22 2012