A053393 Periodic points under the map A053392 that adds consecutive pairs of digits and concatenates them.

0, 991, 992, 993, 994, 995, 996, 997, 998, 999, 1810, 1811, 1812, 1813, 1814, 1815, 1816, 1817, 1818, 6664, 6665, 6666, 6667, 6668, 6669, 33331, 33332, 33333, 33334, 33335, 33336, 121210, 121211, 121212, 121213, 121214, 121215

Offset: 0

Author

Erich Friedman, Jan 07 2000

Keywords

• nonn
• base
• nice
• more

Comments

Apart from 0, the terms listed so far are all of period 2 or 3. Are there longer periods?

Examples

			f(84290) = 126119 since 8+4 = 12, 4+2 = 6, 2+9 = 11, 9+0 = 9.
		

Crossrefs

Cf. A053392.

Programs

Python

def f(n):
  if 0 <= n <= 9: return 0
  d = str(n)
  return int("".join(str(int(di)+int(dj)) for di, dj in zip(d[:-1], d[1:])))
def aupto(limit):
  n, DIVERGENCELIMIT = 0, 10**100
  while n <= limit:
    m, orbit = n, []
    while m <= DIVERGENCELIMIT and m not in orbit: orbit.append(m); m = f(m)
    if m in orbit and m == orbit[0]: print(n, end=", ")
    n += 1
aupto(130000) # Michael S. Branicky, Mar 24 2021

Extensions

More terms from Naohiro Nomoto, Apr 06 2001

0 added by N. J. A. Sloane, Nov 01 2019