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A326538
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a(n) is the numerator of the image of 1/n by the Cantor staircase function.
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2
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 3, 3, 3, 3, 23, 1, 5, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 15, 1, 7, 7
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OFFSET
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1,11
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COMMENTS
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The Cantor staircase function, say c, maps rational numbers in the interval [0..1] to rational numbers in the interval [0..1], hence this sequence is well defined.
For any n > 0, the binary expansion of c(1/n) is terminating (and A326539(n) is a power of 2) iff the ternary expansion of 1/n is terminating or contains a digit 1.
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LINKS
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EXAMPLE
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The first terms, alongside c(1/n) and the ternary and binary representation of 1/n and c(1/n), respectively, with periodic part in parentheses, are:
n a(n) c(1/n) ter(1/n) bin(c(1/n))
-- ---- ------ ---------------------- -----------
1 1 1 1.(0) 1.(0)
2 1 1/2 0.(1) 0.1(0)
3 1 1/2 0.1(0) 0.1(0)
4 1 1/3 0.(02) 0.(01)
5 1 1/4 0.(0121) 0.01(0)
6 1 1/4 0.0(1) 0.01(0)
7 1 1/4 0.(010212) 0.01(0)
8 1 1/4 0.(01) 0.01(0)
9 1 1/4 0.01(0) 0.01(0)
10 1 1/5 0.(0022) 0.(0011)
11 3 3/16 0.(00211) 0.0011(0)
12 1 1/6 0.0(02) 0.0(01)
13 1 1/7 0.(002) 0.(001)
14 1 1/8 0.(001221) 0.001(0)
15 1 1/8 0.0(0121) 0.001(0)
16 1 1/8 0.(0012) 0.001(0)
17 1 1/8 0.(0011202122110201) 0.001(0)
18 1 1/8 0.00(1) 0.001(0)
19 1 1/8 0.(001102100221120122) 0.001(0)
20 1 1/8 0.(0011) 0.001(0)
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PROG
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(PARI) See Links section.
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CROSSREFS
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See A326539 for the corresponding denominators.
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KEYWORD
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nonn,base,frac
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AUTHOR
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STATUS
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approved
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