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 A066711 RATS: Reverse Add Then Sort the digits applied to previous term, starting with 9. 11
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(1) = A114612(1) = 9; A114611(3) = 2. [Reinhard Zumkeller, Mar 14 2012] 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). 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 EXAMPLE 668 -> 668 + 866 = 1534 -> 1345. 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 *) PROG (Haskell) a066711_list = iterate a036839 9 -- Reinhard Zumkeller, Mar 14 2012 (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 CROSSREFS Cf. A004000, A036839, A066710, A033896, A114611, A114612. Cf. A004000, A066710, A209878, A209879, A209880. Sequence in context: A186951 A176201 A186443 * A033651 A050250 A080453 Adjacent sequences: A066708 A066709 A066710 * A066712 A066713 A066714 KEYWORD nonn,base AUTHOR N. J. A. Sloane, Jan 19 2002 STATUS approved

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Last modified December 10 02:09 EST 2022. Contains 358712 sequences. (Running on oeis4.)