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 A383821 #27 May 16 2025 14:34:11 %S A383821 2,5,7,67,75,92,667,792,875,6667,6875,9792,66667,69792,96875,296875, %T A383821 369792,666667,2369792,4296875,6666667,62369792,66666667,262369792, %U A383821 404296875,666666667,6666666667,7262369792,9404296875,27262369792,39404296875,66666666667,639404296875 %N A383821 3-automorphic numbers: positive integers k such that 3k^2 ends with k. %C A383821 All 3-automorphic numbers end in 2, 5, or 7 only. %C A383821 From _Michael S. Branicky_, May 11 2025: (Start) %C A383821 Terms of successively larger digits can be created by prepending digits on the left of previous terms; for each length, only 3 positive such "seeds" are valid (some may have leading zeros and thus do not contribute terms at that length). %C A383821 Infinite since 6..67, with i 6's and then a 7 is a term for all i >= 0. %C A383821 a(2774) has 1001 digits. (End) %H A383821 Michael S. Branicky, <a href="/A383821/b383821.txt">Table of n, a(n) for n = 1..2773</a> %H A383821 Shyam Sunder Gupta, <a href="https://doi.org/10.1007/978-981-97-2465-9_2">Elegance of Squares, Cubes, and Higher Powers</a>, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 2, 29-81. %e A383821 67 is in the sequence because 3*67^2 = 13467 which ends with 67. %t A383821 Select[Range[10^7],IntegerDigits[#]==Take[IntegerDigits[3#^2],-IntegerLength[#]]&] (* _James C. McMahon_, May 16 2025 *) %Y A383821 Cf. A003226, A033428. %Y A383821 Essentially the union of A030985, A030986, and A067275. %K A383821 nonn,base %O A383821 1,1 %A A383821 _Shyam Sunder Gupta_, May 11 2025 %E A383821 More terms from _Michael S. Branicky_, May 11 2025