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
KEYWORD
nonn,base
AUTHOR
Szumi Xie, Sep 18 2022
STATUS
approved