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

1, 11, 110, 11001, 11001011, 1100101101110, 11001011011100111101, 11001011011100111101011000111, 1100101101110011110101100011101110011111, 1100101101110011110101100011101110011111011110101101

Offset

1,2

Comments

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

It is not true that every term is a prefix of the following term; the first counterexample is at the 15th term.

It appears that the lengths of the common prefixes between adjacent terms strictly increase.

Links

Szumi Xie, Table of n, a(n) for n = 1..24

Example

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.

Mathematica

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 *)

Prog

(Haskell)
import Data.List (group)
import Numeric (showBin)
a356329 n = a356329_list !! (n - 1)
a356329_list = read <$> iterate (concat . concatMap (\x -> [take 1 x, showBin (length x) ""]) . group) "1" :: [Integer]
(Python)
from itertools import accumulate, groupby, repeat
def summarize(n, _): return int("".join(k+bin(len(list(g)))[2:] for k, g in groupby(str(n))))
def aupto(terms): return list(accumulate(repeat(1, terms), summarize))
print(aupto(11)) # Michael S. Branicky, Sep 18 2022

Crossrefs

Cf. A001387, A007651.

Sequence in context: A185535 A281601 A266513 * A055016 A259372 A348871

Adjacent sequences: A356326 A356327 A356328 * A356330 A356331 A356332

Keyword

nonn,base

Author

Szumi Xie, Sep 18 2022

Status

approved