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A213723
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a(n) = smallest natural number x such that x=n+A000120(x), otherwise zero.
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18
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0, 2, 0, 4, 6, 0, 0, 8, 10, 0, 12, 14, 0, 0, 0, 16, 18, 0, 20, 22, 0, 0, 24, 26, 0, 28, 30, 0, 0, 0, 0, 32, 34, 0, 36, 38, 0, 0, 40, 42, 0, 44, 46, 0, 0, 0, 48, 50, 0, 52, 54, 0, 0, 56, 58, 0, 60, 62, 0, 0, 0, 0, 0, 64, 66, 0, 68, 70, 0, 0, 72, 74, 0, 76, 78
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OFFSET
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0,2
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LINKS
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FORMULA
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Also, by partitioning into sums of distinct nonzero terms of A000225: if n can be formed as a sum of (2^a)-1 + (2^b)-1 + (2^c)-1, etc. where the exponents a, b, c are distinct and all > 0, then a(n) = 2^a + 2^b + 2^c, etc. If this is not possible, then n is one of the terms of A055938, and a(n)=0.
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EXAMPLE
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a(1) = 2, as 2 is the smallest natural number such that x such that x=1+A000120(x) (as 2=1+A000120(2)=1+1).
a(2) = 0, as there are no solutions for 2, because it belongs to A055938.
a(11) = 14, as 14 is the smallest natural number x such that x=11+A000120(x) (as 14=11+A000120(14)=11+3).
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PROG
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(Haskell)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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