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

Author

N. J. A. Sloane, Jan 19 2002

Keywords

• nonn
• base

Comments

a(1) = A114614(1) = 3; A114611(3) = 8. [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.
• 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).

Crossrefs

Cf. A004000, A036839, A066711, A209878, A209879, A209880.

Programs

Haskell

a066710_list = iterate a036839 3  -- Reinhard Zumkeller, Mar 14 2012

Mathematica

f[k_] := Module[{m = FromDigits[Reverse[IntegerDigits[k]]]}, FromDigits[ Sort[ IntegerDigits[k + m]]]]; NestList[f, 3, 50] (* Harvey P. Dale, Jan 18 2011 *)

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)