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 A066710 RATS: Reverse Add Then Sort the digits applied to previous term, starting with 3. 10
 3, 6, 12, 33, 66, 123, 444, 888, 1677, 3489, 12333, 44556, 111, 222, 444, 888, 1677, 3489, 12333, 44556, 111, 222, 444, 888, 1677, 3489, 12333, 44556, 111, 222, 444, 888, 1677, 3489, 12333, 44556, 111, 222, 444, 888, 1677, 3489, 12333 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(1) = A114614(1) = 3; A114611(3) = 8. [Reinhard Zumkeller, Mar 14 2012] LINKS Table of n, a(n) for n=1..43. R. K. Guy, Conway's RATS and other reversals, Amer. Math. Monthly, 96 (1989), 425-428. Eric Weisstein's World of Mathematics, RATS Sequence Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1). 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 8. a(n+1) = A036839(a(n)). [Reinhard Zumkeller, Mar 14 2012] From Chai Wah Wu, Feb 07 2020: (Start) a(n) = a(n-8) for n > 14. G.f.: x*(-99*x^13 - 45*x^12 - 44523*x^11 - 12321*x^10 - 3483*x^9 - 1674*x^8 - 888*x^7 - 444*x^6 - 123*x^5 - 66*x^4 - 33*x^3 - 12*x^2 - 6*x - 3)/(x^8 - 1). (End) EXAMPLE 668 -> 668 + 866 = 1534 -> 1345. MATHEMATICA f[k_] := Module[{m = FromDigits[Reverse[IntegerDigits[k]]]}, FromDigits[ Sort[ IntegerDigits[k + m]]]]; NestList[f, 3, 50] (* Harvey P. Dale, Jan 18 2011 *) PROG (Haskell) a066710_list = iterate a036839 3 -- Reinhard Zumkeller, Mar 14 2012 CROSSREFS Cf. A004000, A036839, A066711, A209878, A209879, A209880. Sequence in context: A252696 A288147 A026079 * A033648 A102972 A075209 Adjacent sequences: A066707 A066708 A066709 * A066711 A066712 A066713 KEYWORD nonn,base AUTHOR N. J. A. Sloane, Jan 19 2002 STATUS approved

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Last modified August 4 15:45 EDT 2024. Contains 374923 sequences. (Running on oeis4.)