A209880 RATS: Reverse Add Then Sort the digits applied to previous term, starting with 29.

29, 112, 233, 556, 1112, 2233, 5555, 1111, 2222, 4444, 8888, 16777, 34589, 112333, 444455, 889999, 1788899, 1177777, 4558889, 13444447, 77888888, 156667777, 233444489, 1112278888, 11999, 11119, 1223, 4444, 8888, 16777, 34589, 112333, 444455, 889999, 1788899

Offset

1,1

Comments

A114616(1) = 29 is the smallest starting number for a RATS trajectory leading to a cycle of length 18: A114611(29) = 18;

a(n + 18) = a(n) for n > 9.

Links

Table of n, a(n) for n=1..35.

Eric Weisstein's World of Mathematics, RATS Sequence

Index entries for periodic sequences.

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

Formula

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

G.f.: x*(29 + 112*x + 233*x^2 + 556*x^3 + 1112*x^4 + 2233*x^5 + 5555*x^6 + 1111*x^7 + 2222*x^8 + 4444*x^9 + 8888*x^10 + 16777*x^11 + 34589*x^12 + 112333*x^13 + 444455*x^14 + 889999*x^15 + 1788899*x^16 + 1177777*x^17 + 4558860*x^18 + 13444335*x^19 + 77888655*x^20 + 156667221*x^21 + 233443377*x^22 + 1112276655*x^23 + 6444*x^24 + 10008*x^25 - 999*x^26)/(1 - x^18). - Charles R Greathouse IV, May 15 2026

Mathematica

NestList[FromDigits[Sort[IntegerDigits[#+IntegerReverse[#]]]]&, 29, 40] (* or *) PadRight[{29, 112, 233, 556, 1112, 2233, 5555, 1111, 2222}, 50, {4558889, 13444447, 77888888, 156667777, 233444489, 1112278888, 11999, 11119, 1223, 4444, 8888, 16777, 34589, 112333, 444455, 889999, 1788899, 1177777}] (* Harvey P. Dale, Sep 17 2018 *)

Prog

(Haskell)
a209880 n = a209880_list !! (n-1)
a209880_list = iterate a036839 29

Crossrefs

Cf. A004000, A066710, A209878, A066711, A209879.

Sequence in context: A232787 A232852 A233117 * A232784 A232849 A233118

Adjacent sequences: A209877 A209878 A209879 * A209881 A209882 A209883

Keyword

nonn,base,easy

Author

Reinhard Zumkeller, Mar 14 2012

Status

approved