A209880 RATS: Reverse Add Then Sort the digits applied to previous term, starting with 29.

29, 112, 233, 556, 1112, 2233, 5555, 1111, 2222, 4444, 8888, 16777, 34589, 112333, 444455, 889999, 1788899, 1177777, 4558889, 13444447, 77888888, 156667777, 233444489, 1112278888, 11999, 11119, 1223, 4444, 8888, 16777, 34589, 112333, 444455, 889999, 1788899

Offset: 1

Author

Reinhard Zumkeller, Mar 14 2012

Keywords

• nonn
• base

Comments

A114616(1) = 29 is the smallest starting number for a RATS trajectory leading to a cycle of length 18: A114611(29) = 18;

a(n + 18) = a(n) for n > 9.

Links

• Eric Weisstein's World of Mathematics, RATS Sequence
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Crossrefs

Cf. A004000, A066710, A209878, A066711, A209879.

Programs

Haskell

a209880 n = a209880_list !! (n-1)
a209880_list = iterate a036839 29

Mathematica

NestList[FromDigits[Sort[IntegerDigits[#+IntegerReverse[#]]]]&,29,40] (* or *) PadRight[{29,112,233,556,1112,2233,5555,1111,2222},50,{4558889,13444447,77888888,156667777,233444489,1112278888,11999,11119,1223,4444,8888,16777,34589,112333,444455,889999,1788899,1177777}] (* Harvey P. Dale, Sep 17 2018 *)

Formula

a(n + 1) = A036839(a(n)).