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A066710 RATS: Reverse Add Then Sort the digits applied to previous term, starting with 3.

%I A066710 #32 Feb 16 2025 08:32:45
%S A066710 3,6,12,33,66,123,444,888,1677,3489,12333,44556,111,222,444,888,1677,
%T A066710 3489,12333,44556,111,222,444,888,1677,3489,12333,44556,111,222,444,
%U A066710 888,1677,3489,12333,44556,111,222,444,888,1677,3489,12333
%N A066710 RATS: Reverse Add Then Sort the digits applied to previous term, starting with 3.
%C A066710 a(1) = A114614(1) = 3; A114611(3) = 8. [_Reinhard Zumkeller_, Mar 14 2012]
%H A066710 R. K. Guy, <a href="http://www.jstor.org/stable/2325149">Conway's RATS and other reversals</a>, Amer. Math. Monthly, 96 (1989), 425-428.
%H A066710 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RATSSequence.html">RATS Sequence</a>
%H A066710 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,1).
%F A066710 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).
%F A066710 Periodic with period 8.
%F A066710 a(n+1) = A036839(a(n)). [_Reinhard Zumkeller_, Mar 14 2012]
%F A066710 From _Chai Wah Wu_, Feb 07 2020: (Start)
%F A066710 a(n) = a(n-8) for n > 14.
%F A066710 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)
%e A066710 668 -> 668 + 866 = 1534 -> 1345.
%t A066710 f[k_] := Module[{m = FromDigits[Reverse[IntegerDigits[k]]]}, FromDigits[ Sort[ IntegerDigits[k + m]]]]; NestList[f, 3, 50] (* _Harvey P. Dale_, Jan 18 2011 *)
%o A066710 (Haskell)
%o A066710 a066710_list = iterate a036839 3  -- _Reinhard Zumkeller_, Mar 14 2012
%Y A066710 Cf. A004000, A036839, A066711, A209878, A209879, A209880.
%K A066710 nonn,base
%O A066710 1,1
%A A066710 _N. J. A. Sloane_, Jan 19 2002