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A308048
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a(n) = n - nextprime(ceiling(n/2) - 1), where nextprime(n) is the smallest prime > n.
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0
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-1, 0, 1, 2, 2, 3, 2, 3, 4, 5, 4, 5, 6, 7, 4, 5, 6, 7, 8, 9, 10, 11, 10, 11, 12, 13, 10, 11, 12, 13, 14, 15, 16, 17, 16, 17, 18, 19, 16, 17, 18, 19, 20, 21, 22, 23, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 28, 29, 30, 31, 26, 27, 28, 29, 30, 31, 32
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OFFSET
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1,4
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COMMENTS
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For n >= 3, a(n) is the difference of n and the smallest prime appearing among the larger parts of the partitions of n into two parts.
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LINKS
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FORMULA
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a(n) = n - A151800(ceiling(n/2) - 1).
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EXAMPLE
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a(7) = 2; n = 7 has three partitions into two parts: (6,1), (5,2) and (4,3). The smallest prime among the larger parts is 5 and 7 - 5 = 2.
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MATHEMATICA
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Table[n - NextPrime[Ceiling[n/2] - 1, 1], {n, 100}]
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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