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

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

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