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A032937
Numbers k whose base-2 representation Sum_{i=0..m} d(i)*2^(m-i) has d(i)=0 for all odd i, excluding 0. Here m is the position of the leading bit of k.
3
1, 2, 4, 5, 8, 10, 16, 17, 20, 21, 32, 34, 40, 42, 64, 65, 68, 69, 80, 81, 84, 85, 128, 130, 136, 138, 160, 162, 168, 170, 256, 257, 260, 261, 272, 273, 276, 277, 320, 321, 324, 325, 336, 337, 340, 341, 512, 514, 520, 522, 544, 546
OFFSET
1,2
COMMENTS
Essentially the same as A126684. - R. J. Mathar, Jun 15 2008
A126684 is the primary entry for this sequence. - Franklin T. Adams-Watters, Aug 30 2014
MATHEMATICA
Join[{1}, Select[Range[0, 600], Union[Take[IntegerDigits[#, 2], {2, -1, 2}]]=={0}&]] (* Harvey P. Dale, Sep 17 2023 *)
PROG
(Python)
from gmpy2 import digits
def A032937(n):
def bisection(f, kmin=0, kmax=1):
while f(kmax) > kmax: kmax <<= 1
while kmax-kmin > 1:
kmid = kmax+kmin>>1
if f(kmid) <= kmid:
kmax = kmid
else:
kmin = kmid
return kmax
def g(x):
s = digits(x, 4)
for i in range(l:=len(s)):
if s[i]>'1':
break
else:
return int(s, 2)
return int(s[:i]+'1'*(l-i), 2)
def f(x): return n+x-g(x)-g(x>>1)
return bisection(f, n, n) # Chai Wah Wu, Oct 29 2024
CROSSREFS
Sequence in context: A300351 A105425 A199799 * A126684 A089653 A180252
KEYWORD
nonn,base,changed
STATUS
approved