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 A349875 #20 Dec 08 2021 19:58:32
%S A349875 0,1,3,6,78,686999778,9876799878,89996788896,77779987999896,
%T A349875 589598998999878,999699998689998991,9988894989978899995,
%U A349875 95898999989999989765,999999966989999986978996
%N A349875 Triangular numbers whose mean digit value reaches a new maximum.
%C A349875 Subsequence of A068808.
%C A349875 No triangular number ends in 9, so the mean digit value is always less than 9.
%C A349875 Is this sequence finite? Or does the mean digit value approach some upper limit arbitrarily closely without ever reaching it exactly, and, if so, what is that limit?
%C A349875 a(14) <= 999999966989999986978996. - _David A. Corneth_, Dec 05 2021
%e A349875 n a(n) digit sum #dgts mean digit value
%e A349875 -- -------------------- --------- ----- ----------------
%e A349875 1 0 0 1 0
%e A349875 2 1 1 1 1
%e A349875 3 3 3 1 3
%e A349875 4 6 6 1 6
%e A349875 5 78 15 2 7.5
%e A349875 6 686999778 69 9 7.66666666666...
%e A349875 7 9876799878 78 10 7.8
%e A349875 8 89996788896 87 11 7.90909090909...
%e A349875 9 77779987999896 111 14 7.92857142857...
%e A349875 10 589598998999878 120 15 8
%e A349875 11 999699998689998991 145 18 8.05555555555...
%e A349875 12 9988894989978899995 154 19 8.10526315789...
%e A349875 13 95898999989999989765 163 20 8.15
%t A349875 seq = {}; max = -1; Do[If[(m = Mean @ IntegerDigits[(t = n*(n + 1)/2)]) > max, max = m; AppendTo[seq, t]], {n, 0, 10^6}]; seq (* _Amiram Eldar_, Dec 03 2021 *)
%o A349875 (Python)
%o A349875 def meandigval(n): s = str(n); return sum(map(int, s))/len(s)
%o A349875 def afind(limit):
%o A349875 alst, k, t, record = [], 0, 0, -1
%o A349875 while t <= limit:
%o A349875 mdv = meandigval(t)
%o A349875 if mdv > record:
%o A349875 print(t, end=", ")
%o A349875 record = mdv
%o A349875 k += 1
%o A349875 t += k
%o A349875 afind(10**14) # _Michael S. Branicky_, Dec 03 2021
%Y A349875 Cf. A000217, A068133, A068808, A069669, A069670, A095864.
%K A349875 nonn,base,hard,more
%O A349875 1,3
%A A349875 _Jon E. Schoenfield_, Dec 03 2021
%E A349875 a(14) verified by _Martin Ehrenstein_, Dec 06 2021