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 A338767 #13 Nov 18 2020 21:32:55
%S A338767 0,1,3,6,10,65,1211,8988,16171616,1015101610151015,
%T A338767 11101115111011161110111511101115,
%U A338767 1212121112121216121212111212121712121211121212161212121112121216
%N A338767 a(0) = 0; a(n) is obtained by incrementing each digit of a(n-1) by n.
%C A338767 This sequence is the additive counterpart of the digit factorials which, unlike the digit factorials, increases at a faster pace. A061511 and its relatives bear similarities to this sequence, but each of these increase at varying rates depending on the chosen constant. However, unlike these sequences, the constant increases by 1 each time. If digits within a(n-1) exceed 9 when one adds a constant, we ignore carrying and replace the digit with its correct value, thus 9+1 = 10. a(15) has 1024 digits.
%e A338767 a(5) = {1+5, 0+5} = 65, where {x, y} is the concatenation of x and y.
%e A338767 a(6) = {6+6, 5+6} = 1211.
%p A338767 a:= proc(n) option remember; `if`(n=0, 0, (l-> parse(cat(
%p A338767 seq(n+l[-i], i=1..nops(l)))))(convert(a(n-1), base, 10)))
%p A338767 end:
%p A338767 seq(a(n), n=0..12); # _Alois P. Heinz_, Nov 15 2020
%t A338767 Nest[Append[#1, FromDigits@ Apply[Join, Map[IntegerDigits, IntegerDigits[#1[[-1]] ] + #2]]] & @@ {#, Length@ #} &, {0}, 11] (* _Michael De Vlieger_, Nov 13 2020 *)
%Y A338767 Cf. A061511-A061750, A061581-A061587, A089718, A337770.
%K A338767 nonn,base
%O A338767 0,3
%A A338767 _Jamie Robert Creasey_, Nov 07 2020