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 A053393 #22 May 19 2021 00:10:48
%S A053393 0,991,992,993,994,995,996,997,998,999,1810,1811,1812,1813,1814,1815,
%T A053393 1816,1817,1818,6664,6665,6666,6667,6668,6669,33331,33332,33333,33334,
%U A053393 33335,33336,121210,121211,121212,121213,121214,121215
%N A053393 Periodic points under the map A053392 that adds consecutive pairs of digits and concatenates them.
%C A053393 Apart from 0, the terms listed so far are all of period 2 or 3. Are there longer periods?
%e A053393 f(84290) = 126119 since 8+4 = 12, 4+2 = 6, 2+9 = 11, 9+0 = 9.
%o A053393 (Python)
%o A053393 def f(n):
%o A053393 if 0 <= n <= 9: return 0
%o A053393 d = str(n)
%o A053393 return int("".join(str(int(di)+int(dj)) for di, dj in zip(d[:-1], d[1:])))
%o A053393 def aupto(limit):
%o A053393 n, DIVERGENCELIMIT = 0, 10**100
%o A053393 while n <= limit:
%o A053393 m, orbit = n, []
%o A053393 while m <= DIVERGENCELIMIT and m not in orbit: orbit.append(m); m = f(m)
%o A053393 if m in orbit and m == orbit[0]: print(n, end=", ")
%o A053393 n += 1
%o A053393 aupto(130000) # _Michael S. Branicky_, Mar 24 2021
%Y A053393 Cf. A053392.
%K A053393 nonn,base,nice,more
%O A053393 0,2
%A A053393 _Erich Friedman_, Jan 07 2000
%E A053393 More terms from _Naohiro Nomoto_, Apr 06 2001
%E A053393 0 added by _N. J. A. Sloane_, Nov 01 2019