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A175851
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a(n) = 1 for noncomposite n, a(n) = n - previousprime(n) + 1 for composite n.
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14
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1, 1, 1, 2, 1, 2, 1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 1, 2, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 1, 2, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 1, 2, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4
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OFFSET
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1,4
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COMMENTS
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Sequence is cardinal and not fractal. Cardinal sequence is sequence with infinitely many times occurring all natural numbers. Fractal sequence is sequence such that when the first instance of each number in the sequence is erased, the original sequence remains.
Ordinal transform of the nextprime function, A151800(1..) = 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, ..., also ordinal transform of A304106. - Antti Karttunen, Jun 09 2018
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LINKS
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FORMULA
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a(1) = 1, a(n) = n - A007917(n) + 1 for n >= 2. a(1) = 1, a(2) = 1, a(n) = n - A151799(n+1) + 1 for n >= 3.
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MATHEMATICA
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a[n_] := If[!CompositeQ[n], 1, n - NextPrime[n, -1] + 1];
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PROG
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CROSSREFS
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Cf. A065358 for another way of visualizing prime gaps.
Cf. A304106 (ordinal transform of this sequence).
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KEYWORD
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AUTHOR
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STATUS
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approved
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