A066711 RATS: Reverse Add Then Sort the digits applied to previous term, starting with 9.

9, 18, 99, 189, 117, 288, 117, 288, 117, 288, 117, 288, 117, 288, 117, 288, 117, 288, 117, 288, 117, 288, 117, 288, 117, 288, 117, 288, 117, 288, 117, 288, 117, 288, 117, 288, 117, 288, 117, 288, 117, 288, 117, 288, 117, 288, 117, 288, 117

Offset: 1

Author

N. J. A. Sloane, Jan 19 2002

Keywords

• nonn
• base

Comments

a(1) = A114612(1) = 9; A114611(3) = 2. - Reinhard Zumkeller, Mar 14 2012

Examples

			668 -> 668 + 866 = 1534 -> 1345.
		

Links

• R. K. Guy, Conway's RATS and other reversals, Amer. Math. Monthly, 96 (1989), 425-428.
• J. Thiel, Conway’s RATS Sequences in Base 3, Journal of Integer Sequences, 15 (2012), #12.9.2. - _N. J. A. Sloane_, Jan 02 2013
• Eric Weisstein's World of Mathematics, RATS Sequence
• Index entries for linear recurrences with constant coefficients, signature (0,1).

Crossrefs

Cf. A004000, A036839, A066710, A033896, A114611, A114612.

Cf. A004000, A066710, A209878, A209879, A209880.

Programs

Haskell

a066711_list = iterate a036839 9  -- Reinhard Zumkeller, Mar 14 2012

Mathematica

NestList[ FromDigits[ Sort[ IntegerDigits[# + FromDigits[ Reverse[ IntegerDigits[#]]]]]] &, 9, 48] (* Jayanta Basu, Aug 13 2013 *)
Join[{9, 18, 99, 189},LinearRecurrence[{0, 1},{117, 288},45]] (* Ray Chandler, Aug 25 2015 *)

Python

from itertools import accumulate
def rats(anm1, _):
    return int("".join(sorted(str(anm1 + int(str(anm1)[::-1])))))
print(list(accumulate([9]*49, rats))) # Michael S. Branicky, Sep 18 2021

Formula

Let a(n) = k, form m by Reversing the digits of k, Add m to k Then Sort the digits of the sum into increasing order to get a(n+1).

Periodic with period 2.

a(n+1) = A036839(a(n)). - Reinhard Zumkeller, Mar 14 2012

G.f.: x*(-99*x^5 - 18*x^4 - 171*x^3 - 90*x^2 - 18*x - 9)/(x^2 - 1). - Chai Wah Wu, Feb 07 2020