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A102820
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Number of primes between 2*prime(n) and 2*prime(n+1), where prime(n) is the n-th prime.
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9
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1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 3, 1, 1, 1, 3, 3, 0, 2, 2, 0, 3, 1, 2, 4, 2, 0, 1, 0, 1, 6, 1, 3, 1, 3, 0, 3, 1, 1, 1, 3, 1, 3, 1, 1, 1, 4, 4, 1, 1, 2, 1, 1, 3, 2, 2, 0, 1, 1, 1, 1, 3, 6, 2, 0, 1, 6, 1, 3, 0, 1, 1, 3, 2, 2, 1, 2, 1, 1, 2, 4, 1, 3, 1, 1, 2, 1, 2, 1, 0, 1, 4, 2, 1, 3, 0, 2, 5, 0, 5, 3, 3, 2, 1, 0, 2
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OFFSET
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1,3
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COMMENTS
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A080192 lists prime(n) corresponding to the zero terms.
A104380(k) is prime(n) corresponding to the first occurrence of k as a term.
If a(n) is nonzero, A059786(n) is the smallest and A059788(n+1) the largest of the a(n) enumerated primes. In the tree of primes described in A290183, these primes label the child nodes of prime(n).
Conjecture: the asymptotic proportions of 0's, 1's, ... , k's, ... are 1/3, 2/9, ... , 2^k/3^(k+1), ... .
(End)
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LINKS
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FORMULA
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EXAMPLE
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a(15)=3 because there are 3 primes between the doubles of the 15th and 16th primes, that is between 2*47 and 2*53.
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MATHEMATICA
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Table[PrimePi[2 Prime[n+1]]-PrimePi[2 Prime[n]], {n, 150}] (* Zak Seidov *)
Differences[PrimePi[2 Prime[Range[110]]]] (* Harvey P. Dale, Oct 29 2022 *)
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PROG
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(Haskell)
a102820 n = a102820_list !! (n-1)
a102820_list = map (sum . (map a010051)) $
zipWith enumFromTo a100484_list (tail a100484_list)
(PARI) a(n) = primepi(2*prime(n+1)) - primepi(2*prime(n)); \\ Michel Marcus, Sep 22 2017
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Ali A. Tanara (tanara(AT)khayam.ut.ac.ir), Feb 27 2005
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EXTENSIONS
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STATUS
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approved
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