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 A383939 #22 Aug 24 2025 17:46:27
%S A383939 0,28,40,64,400,2828,4000,4064,6428,22840,24028,40000,202428,240028,
%T A383939 400000,2040040,2400028,4000000,6422840,6428064,6646624,20044064,
%U A383939 20202080,20400040,20406080,24000028,40000000,66400064,200042428,204000040,228406080,240000028
%N A383939 Numbers k such that k and the k-th triangular number T(k) = k*(k+1)/2 have only even digits.
%C A383939 The sequence also contains the infinite subsequence 4*10^n for n >= 1.
%H A383939 Shyam Sunder Gupta, <a href="https://doi.org/10.1007/978-981-97-2465-9_3">Triangular Numbers</a>, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 3, 82-125.
%e A383939 64 is a term since it and T(64) = 2080 both have only even digits.
%t A383939 q[k_] := And @@ (AllTrue[IntegerDigits[#], EvenQ] & /@ {k, k*(k+1)/2}); Select[Range[0, 4*10^6], q] (* _Amiram Eldar_, Aug 18 2025 *)
%Y A383939 Cf. A000217, A014263, A117978, A347475.
%K A383939 nonn,base,new
%O A383939 1,2
%A A383939 _Shyam Sunder Gupta_, Aug 18 2025