A380372 Characteristic function of A082851.

1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0

Offset

1

Comments

This sequence is the limit S(infinity) of replications starting S(0) = {} and then S(k) = {S(k-1), S(k-1), 0,0,…,0,1} where the 0,...,0,1 run is k terms long (k-1 0's followed by a 1).

Runs of terms 0,...,0,1 have lengths A082850.

Links

Paolo Xausa, Table of n, a(n) for n = 1..16369

Example

The S construction of for instance S(3), which is terms a(1) to a(11), is
   S(3) = 1,1,0,1, 1,1,0,1, 0,0,1
          \-----/  \-----/  \---/
            S(2)     S(2)   run of 3
Runs of 0,...,0,1 with lengths A082850 begin
  sequence = 1, 1, 0,1, 1, 1, 0,1, 0,0,1, ...
  A082850  = 1  1  2    1  1  2    3

Mathematica

Fold[Flatten[{#, #, PadLeft[{1}, #2]}] &, {}, Range[6]] (* Paolo Xausa, Feb 10 2025 *)

Prog

(Python)
from itertools import count, islice
def A380372_gen():
    S = []
    for n in count(1):
        yield from (m:=S+[0]*(n-1)+[1])
        S += m
A380372 = list(islice(A380372_gen(), 100))

Crossrefs

Cf. A082850, A082851.

Sequence in context: A249066 A176178 A267778 * A379952 A285384 A165728

Adjacent sequences: A380369 A380370 A380371 * A380373 A380374 A380375

Keyword

nonn,new

Author

Jwalin Bhatt, Jan 23 2025

Status

approved