A209878 RATS: Reverse Add Then Sort the digits applied to previous term, starting with 20169.

20169, 111267, 337788, 1122255, 4446666, 1111113, 2222244, 4446666, 1111113, 2222244, 4446666, 1111113, 2222244, 4446666, 1111113, 2222244, 4446666, 1111113, 2222244, 4446666, 1111113, 2222244, 4446666, 1111113, 2222244, 4446666, 1111113, 2222244, 4446666

Offset

1,1

Comments

A114613(1) = 20169 is the smallest starting number for a RATS trajectory leading to a cycle of length 3: A114611(20169) = 3;

a(n + 3) = a(n) for n > 4.

Links

Table of n, a(n) for n=1..29.

Eric Weisstein's World of Mathematics, RATS Sequence

Index entries for periodic sequences.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 1).

Formula

a(n + 1) = A036839(a(n)).

G.f.: x*(20169 + 111267*x + 337788*x^2 + 1102086*x^3 + 4335399*x^4 + 773325*x^5 + 1099989*x^6)/(1 - x^3). - Charles R Greathouse IV, May 15 2026

Mathematica

Join[{20169, 111267, 337788, 1122255}, LinearRecurrence[{0, 0, 1}, {4446666, 1111113, 2222244}, 25]] (* Ray Chandler, Aug 25 2015 *)

Prog

(Haskell)
a209878 n = a209878_list !! (n-1)
a209878_list = iterate a036839 20169
(PARI) a(n)=if(n>4, [1111113, 2222244, 4446666][n%3+1], [20169, 111267, 337788, 1122255][n]) \\ Charles R Greathouse IV, May 15 2026

Crossrefs

Cf. A004000, A066710, A066711, A209879, A209880.

Sequence in context: A235520 A235651 A114613 * A031682 A052358 A052189

Adjacent sequences: A209875 A209876 A209877 * A209879 A209880 A209881

Keyword

nonn,base,easy

Author

Reinhard Zumkeller, Mar 14 2012

Status

approved