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

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

Offset: 1

Author

Szumi Xie, Sep 18 2022

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A001387, A007651.

Programs

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]

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 *)

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