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A022488 Describe previous term from the right (method B - initial term is 2).

%I A022488 #28 Dec 02 2024 16:54:05
%S A022488 2,21,1121,112112,21122112,2112221221,112211231221,1122113121122212,
%T A022488 21112312211131122212,211123123113221131211321,
%U A022488 112131122111311222311231211131211321,112131122111311321113121123123123113221231112112
%N A022488 Describe previous term from the right (method B - initial term is 2).
%C A022488 Method B = 'digit'-indication followed by 'frequency'.
%H A022488 Reinhard Zumkeller, <a href="/A022488/b022488.txt">Table of n, a(n) for n = 1..22</a>
%e A022488 E.g., the term after 1121 is obtained by saying "1 once, 2 once, 1 twice", which gives 112112.
%t A022488 A022488[1]:=2;A022488[n_]:=A022488[n]=FromDigits[Flatten[{First[#],Length[#]}&/@Split[Reverse[IntegerDigits[A022488[n-1]]]]]];Map[A022488,Range[15]] (* _Peter J. C. Moses_, Apr 22 2013 *)
%o A022488 (Haskell)
%o A022488 import Data.List (group, transpose)
%o A022488 a022488 n = a022488_list !! (n-1)
%o A022488 a022488_list = 2 : f [2] :: [Integer] where
%o A022488    f xs = (read $ concatMap show ys) : f ys where
%o A022488           ys = concat $ transpose [map head zss, map length zss]
%o A022488           zss = reverse $ group xs
%o A022488 -- _Reinhard Zumkeller_, Apr 14 2014
%o A022488 (Python)
%o A022488 from re import split
%o A022488 A022488_list, l = [2], '2'
%o A022488 for _ in range(10):
%o A022488     l = ''.join(d[0]+str(len(d)) for d in split('(0+|1+|2+|3+|4+|5+|6+|7+|8+|9+)',l[::-1]) if d != '')
%o A022488     A022488_list.append(int(l)) # _Chai Wah Wu_, Jan 07 2015
%o A022488 (Python)
%o A022488 from itertools import accumulate, groupby, repeat
%o A022488 def summarize(n, _):
%o A022488   return int("".join(k+str(len(list(g))) for k, g in groupby(str(n)[::-1])))
%o A022488 def aupton(nn): return list(accumulate(repeat(2, nn), summarize))
%o A022488 print(aupton(12)) # _Michael S. Branicky_, Feb 21 2021
%Y A022488 Cf. A022481, A022514, A022515, A022516, A022517, A022518, A022519, A022520.
%K A022488 nonn,base,easy,nice
%O A022488 1,1
%A A022488 _Clark Kimberling_