A354680 Terms of A354169 that are not powers of 2, in order of appearance.

0, 3, 12, 17, 34, 68, 136, 768, 1025, 18, 2080, 12288, 16388, 72, 32896, 196608, 262400, 524800, 1048577, 2098176, 4194306, 48, 8390656, 50331648, 67112960, 134225920, 268435460, 536887296, 1073741832, 192, 2147516416, 12884901888, 17179934720, 34359869440

Offset

1,2

Comments

Apart from the initial 0, all terms have Hamming weight 2. See De Vlieger et al. (2022). - N. J. A. Sloane, Aug 29 2022

Links

Rémy Sigrist, Table of n, a(n) for n = 1..3320

Michael De Vlieger, Thomas Scheuerle, Rémy Sigrist, N. J. A. Sloane, and Walter Trump, The Binary Two-Up Sequence, arXiv:2209.04108 [math.CO], Sep 11 2022.

Rémy Sigrist, PARI program

Rémy Sigrist, PARI program (optimized version)

Formula

A000120(A354169(a(n))) <> 1.

Example

The initial terms of A354169 are:
  0, 1, 2, 4, 8, 3, 16, 32, 64, 12, 128, 256.
The initial terms of this sequence are therefore: 0,             3,             12.
and the initial terms of A354798 are
  0,             5,              9.

Prog

(PARI) See Links section.
(Python)
from itertools import count, islice
from collections import deque
from functools import reduce
from operator import or_
def A354680_gen(): # generator of terms
    aset, aqueue, b, f = {0, 1, 2}, deque([2]), 2, False
    yield 0
    while True:
        for k in count(1):
            m, j, j2, r, s = 0, 0, 1, b, k
            while r > 0:
                r, q = divmod(r, 2)
                if not q:
                    s, y = divmod(s, 2)
                    m += y*j2
                j += 1
                j2 *= 2
            if s > 0:
                m += s*2**b.bit_length()
            if m not in aset:
                if m.bit_count() > 1:
                    yield m
                aset.add(m)
                aqueue.append(m)
                if f: aqueue.popleft()
                b = reduce(or_, aqueue)
                f = not f
                break
A354680_list = list(islice(A354680_gen(), 40)) # Chai Wah Wu, Jun 06 2022

Crossrefs

Cf. A000120, A057716, A354169, A354798 (corresponding indices).

See also A354767.

Sequence in context: A082965 A045549 A103249 * A047906 A342776 A104641

Adjacent sequences: A354677 A354678 A354679 * A354681 A354682 A354683

Keyword

nonn,base

Author

Rémy Sigrist and N. J. A. Sloane, Jun 06 2022

Status

approved