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A354680
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Terms of A354169 that are not powers of 2, in order of appearance.
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10
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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
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OFFSET
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1,2
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COMMENTS
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Apart from the initial 0, all terms have Hamming weight 2. See De Vlieger et al. (2022). - N. J. A. Sloane, Aug 29 2022
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LINKS
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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.
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FORMULA
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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