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A179329
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Number of iterations of (n + lpf(n)) / 2 required to reach a prime, where lpf equals the least prime factor.
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1
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0, 0, 1, 0, 2, 0, 1, 3, 3, 0, 1, 0, 2, 4, 4, 0, 4, 0, 1, 2, 2, 0, 1, 5, 3, 5, 5, 0, 5, 0, 1, 5, 5, 2, 1, 0, 2, 3, 3, 0, 3, 0, 1, 2, 2, 0, 6, 6, 4, 6, 6, 0, 6, 6, 1, 6, 6, 0, 1, 0, 2, 6, 6, 3, 6, 0, 3, 2, 2, 0, 1, 0, 3, 4, 4, 4, 4, 0, 1, 4, 4, 0, 1, 3, 2, 3, 3, 0, 3, 7, 1, 7, 7, 5, 7, 0, 5, 7, 7, 0, 7, 0, 1, 7, 7
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OFFSET
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2,5
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COMMENTS
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Zeros indicate prime indices.
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LINKS
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EXAMPLE
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a(15) gives (15 + 3) / 2 = 9, (9 + 3) / 2 = 6, (6 + 2) / 2 = 4, (4 + 2) / 2 = 3. Four iterations were required to reach a prime, so a(15) = 4.
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MATHEMATICA
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f[n_] := Length@ NestWhileList[(# + FactorInteger[#][[1, 1]])/2 &, n, ! PrimeQ@ # &] - 1; Array[f, 105, 2]
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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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