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

0,2

Comments

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

Links

Table of n, a(n) for n=0..36.

Example

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

Prog

(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

Crossrefs

Cf. A053392.

Sequence in context: A119077 A119057 A218401 * A031790 A137703 A255098

Adjacent sequences: A053390 A053391 A053392 * A053394 A053395 A053396

Keyword

nonn,base,nice,more

Author

Erich Friedman, Jan 07 2000

Extensions

More terms from Naohiro Nomoto, Apr 06 2001

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

Status

approved