A082850 Let S(0) = {}, S(n) = {S(n-1), S(n-1), n}; sequence gives S(infinity).

1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 4, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 4, 5, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 4, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 4, 5, 6, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 4, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 4, 5, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1

Offset

1,3

Comments

Sequence counts up to successive values of A001511; i.e., apply the morphism k -> 1,2,...,k to A001511. If all 1's are removed from the sequence, the resulting sequence b has b(n) = a(n)+1. A101925 lists the positions of 1's in this sequence.

Links

Table of n, a(n) for n=1..105.

Formula

a(2^m - 1) = m.

If n = 2^m - 1 + k with 0 < k < 2^m, then a(n) = a(k). - Franklin T. Adams-Watters, Aug 16 2006

a(n) = log_2(A182105(n)) + 1. - Laurent Orseau, Jun 18 2019

Example

S(1) = {1}, S(2) = {1,1,2}, S(3) = {1,1,2,1,1,2,3}, etc.

Mathematica

Fold[Flatten[{#1, #1, #2}] &, {}, Range[5]] (* Birkas Gyorgy, Apr 13 2011 *)
Flatten[Table[Length@Last@Split@IntegerDigits[2 n, 2], {n, 20}] /. {n_ ->Range[n]}] (* Birkas Gyorgy, Apr 13 2011 *)

Prog

(Python)
S = []; [S.extend(S + [n]) for n in range(1, 8)]
print(S) # Michael S. Branicky, Jul 02 2022
(Python)
from itertools import count, islice
def A082850_gen(): # generator of terms
    S = []
    for n in count(1):
        yield from (m:=S+[n])
        S += m #
A082850_list = list(islice(A082850_gen(), 20)) # Chai Wah Wu, Mar 06 2023

Crossrefs

Cf. A082851 (partial sums).

Cf. A001511, A101925.

Sequence in context: A116361 A106796 A265743 * A290695 A277446 A334029

Adjacent sequences: A082847 A082848 A082849 * A082851 A082852 A082853

Keyword

nonn,hear

Author

Benoit Cloitre, Apr 14 2003

Status

approved