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A300475
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a(n) is the least positive k such that the binary representation n appears in front of the binary representation of 1/k (ignoring the radix point and the leading zeros and adding trailing zeros if necessary in case of a terminating expansion).
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3
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1, 1, 5, 1, 3, 5, 9, 1, 7, 3, 11, 5, 19, 9, 17, 1, 15, 7, 13, 25, 3, 23, 11, 21, 5, 19, 37, 9, 35, 17, 33, 1, 31, 15, 29, 7, 27, 53, 13, 25, 49, 3, 47, 23, 45, 11, 43, 21, 41, 81, 5, 39, 19, 75, 37, 9, 71, 35, 69, 17, 67, 33, 65, 1, 63, 31, 61, 15, 59, 29, 57
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OFFSET
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1,3
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COMMENTS
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In other words, a(n) is the least k > 0 such that floor((2^i) / k) = n for some integer i >= 0.
This sequence is similar to A095156 for the base 2.
All terms are odd.
All terms appears infinitely many times (as a(n) equals at least a(2*n) or a(2*n + 1)).
See also A300428 for a similar sequence.
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LINKS
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FORMULA
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a(2^k) = 1 for any k >= 0.
a(2^k - 1) = 2^k + 1 for any k > 1.
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EXAMPLE
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The first terms, alongside the binary representation of 1/a(n) with the earliest occurrence of the binary representation of n in parentheses, are:
n a(n) bin(1/a(n))
-- ---- -----------
1 1 (1).000...
2 1 (1.0)000...
3 5 0.00(11)001...
4 1 (1.00)000...
5 3 0.0(101)010...
6 5 0.00(110)011...
7 9 0.000(111)000...
8 1 (1.000)000...
9 7 0.00(1001)001...
10 3 0.0(1010)101...
11 11 0.000(1011)101...
12 5 0.00(1100)110...
13 19 0.0000(1101)011...
14 9 0.000(1110)001...
15 17 0.0000(1111)000...
16 1 (1.0000)000...
17 15 0.000(10001)000...
18 7 0.00(10010)010...
19 13 0.000(10011)101...
20 25 0.0000(10100)011...
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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