cp's OEIS Frontend

A356329 Binary Look and Say sequence (method B - initial term is 1).

%I A356329 #49 Oct 09 2022 05:22:16
%S A356329 1,11,110,11001,11001011,1100101101110,11001011011100111101,
%T A356329 11001011011100111101011000111,
%U A356329 1100101101110011110101100011101110011111,1100101101110011110101100011101110011111011110101101
%N A356329 Binary Look and Say sequence (method B - initial term is 1).
%C A356329 Method B = 'digit'-indication followed by 'frequency' in binary.
%C A356329 It is not true that every term is a prefix of the following term; the first counterexample is at the 15th term.
%C A356329 It appears that the lengths of the common prefixes between adjacent terms strictly increase.
%H A356329 Szumi Xie, <a href="/A356329/b356329.txt">Table of n, a(n) for n = 1..24</a>
%e A356329 The term after 11001 is obtained by saying "1 twice (10 in binary), 0 twice (10) and 1 once (1)", giving 1 10 0 10 1 1.
%t A356329 a[1]=1; a[n_] := a[n]=Block[{s = Split@ IntegerDigits@ a[n-1]}, FromDigits@ Flatten@ Transpose[{First /@ s, IntegerDigits[ Length /@ s, 2]}]]; Array[a, 10] (* _Giovanni Resta_, Oct 05 2022 *)
%o A356329 (Haskell)
%o A356329 import Data.List (group)
%o A356329 import Numeric (showBin)
%o A356329 a356329 n = a356329_list !! (n - 1)
%o A356329 a356329_list = read <$> iterate (concat . concatMap (\x -> [take 1 x, showBin (length x) ""]) . group) "1" :: [Integer]
%o A356329 (Python)
%o A356329 from itertools import accumulate, groupby, repeat
%o A356329 def summarize(n, _): return int("".join(k+bin(len(list(g)))[2:] for k, g in groupby(str(n))))
%o A356329 def aupto(terms): return list(accumulate(repeat(1, terms), summarize))
%o A356329 print(aupto(11)) # _Michael S. Branicky_, Sep 18 2022
%Y A356329 Cf. A001387, A007651.
%K A356329 nonn,base
%O A356329 1,2
%A A356329 _Szumi Xie_, Sep 18 2022