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A354680
Terms of A354169 that are not powers of 2, in order of appearance.
10
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
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
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 3.10+)
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
KEYWORD
nonn,base
AUTHOR
STATUS
approved