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Periodic points under the map A053392 that adds consecutive pairs of digits and concatenates them.
3

%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