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