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A372680
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Integers k such that 2^k contains all powers of 2 not exceeding k as substrings.
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0
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124, 192, 322, 808, 830, 957, 1757, 4067, 5489, 6616, 6724, 6794, 7065, 7727, 7728, 7736, 8253, 8938, 9438, 9989, 10194, 10195, 10271, 10350, 10389, 10397, 10445, 10475, 10611, 10835, 11107, 11500, 11606, 11758, 11835, 12089, 12304, 12398, 12501, 12548, 12645, 12694, 12695, 12734, 12820
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OFFSET
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1,1
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COMMENTS
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It is unknown whether this sequence contains infinitely many terms.
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LINKS
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EXAMPLE
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124 is a term; 2^124 = 21267647932558653966460912964485513216 contains 2, 4, 8, 16, 32, 64 as substrings.
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PROG
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(Python)
def f(m):
a = str(2**m)
for i in range(0, m.bit_length()):
if str(2**i) not in a:
return 0
return 1
def a(n):
m = 0
i = 0
while i != n:
m += 1
i += f(m)
return m
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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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