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Search: id:A107483
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| A107483 |
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Base 3 representation of the positive integers n such that Sum[d[k],k=1..n] is an integer, where d(k) is the base 3 fraction 0.k (e.g., d(22 base 10)=d(211 base 3)=0.221 base 3. |
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1
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| 2, 20, 100, 122, 2222, 20000, 100000, 122222, 2222222, 20000000, 100000000, 122222222, 2222222222, 20000000000, 100000000000, 122222222222, 2222222222222, 20000000000000, 100000000000000, 122222222222222
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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It appears that a(n)=2*(3^(3*k-1))-1 if n=4k, a(n)=3^(3*k+1)-1 if n=4k+1, a(n)=2*(3^(3*k+1)) if n=4k+2, and a(n)=3^(3*k+2) if n=4k+3.
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EXAMPLE
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Sum[d(k), k=1..6](base 3) = (0.1+0.2+0.10+0.11+0.12+0.20)(base 3)=10.0 (base 3)=3 (base 10), hence 6 is in the sequence.
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CROSSREFS
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Cf. A054464.
Sequence in context: A069187 A033840 A086755 this_sequence A035599 A103101 A009357
Adjacent sequences: A107480 A107481 A107482 this_sequence A107484 A107485 A107486
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Jun 09 2005
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