A209879 RATS: Reverse Add Then Sort the digits applied to previous term, starting with 6999.

6999, 15699, 11355, 66666, 123333, 445566, 111111, 222222, 444444, 888888, 1677777, 3455589, 11112333, 33444444, 77778888, 156666666, 123333378, 666669999, 1356666666, 123333789, 11111667, 22777788, 11115555, 66666666, 123333333, 445566666, 111122223

Offset: 1

Author

Reinhard Zumkeller, Mar 14 2012

Keywords

• nonn
• base

Comments

A114615(1) = 6999 is the smallest starting number for a RATS trajectory leading to a cycle of length 14: A114611(6999) = 14;

a(n + 14) = a(n) for n > 25.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..100
• Eric Weisstein's World of Mathematics, RATS Sequence
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Crossrefs

Cf. A004000, A066710, A209878, A066711, A209880.

Programs

Haskell

a209879 n = a209879_list !! (n-1)
a209879_list = iterate a036839 6999

Mathematica

rats[n_]:=Module[{idnr=FromDigits[Reverse[IntegerDigits[n]]]}, FromDigits[ Sort[ IntegerDigits[idnr+n]]]]; NestList[rats,6999,30] (* Harvey P. Dale, May 29 2014 *)

Formula

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