A022481 Describe previous term from the right (method B - initial term is 1).

1, 11, 12, 2111, 1321, 11213111, 1331112112, 211221133211, 12213212221221, 11221123112131112211, 122213311121123121122212, 211123122111312112211332112311

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base
• easy
• nice

Comments

Method B = 'digit'-indication followed by 'frequency'.

Examples

			E.g. the term after 1321 is obtained by saying "1 once, 2 once, 3 once, 1 once", which gives 11213111.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..24

Crossrefs

Cf. A022488, A022514, A022515, A022516, A022517, A022518, A022519, A022520.

Programs

Haskell

import Data.List (group, transpose)
a022481 n = a022481_list !! (n-1)
a022481_list = 1 : f [1] :: [Integer] where
   f xs = (read $ concatMap show ys) : f ys where
          ys = concat $ transpose [map head zss, map length zss]
          zss = reverse $ group xs
-- Reinhard Zumkeller, Jan 26 2014

Mathematica

A022481[1]:=1;A022481[n_]:=A022481[n]=FromDigits[Flatten[{First[#],Length[#]}&/@Split[Reverse[IntegerDigits[A022481[n-1]]]]]];Map[A022481,Range[15]] (* Peter J. C. Moses, Apr 22 2013 *)
a[1]=1;a[n_]:=a[n]=FromDigits[Flatten[Replace[ Replace[ Replace[ Split[ Reverse[IntegerDigits[a[n-1]]]],{x_,y_}->{x,Length[{x,y}]},{1}],{x_,y_,z_}->{x,Length[{x,y,z}]},{1}],{x_}->{x,Length[{x}]},{1}]]];Array[a,15] (* Ivan N. Ianakiev, Jun 22 2017 *)
NestList[FromDigits@ Flatten@ Reverse@ Map[{First@ #, Length@ #} &, Split@ IntegerDigits@ #] &, 1, 11] (* Michael De Vlieger, Jun 26 2017 *)