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A070046
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Number of primes between prime(n) and 2*prime(n) exclusive.
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8
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1, 1, 1, 2, 3, 3, 4, 4, 5, 6, 7, 9, 9, 9, 9, 11, 13, 12, 13, 14, 13, 15, 15, 16, 19, 20, 19, 19, 18, 18, 23, 23, 25, 25, 27, 26, 28, 28, 28, 28, 30, 30, 32, 32, 32, 32, 35, 38, 38, 38, 39, 39, 39, 41, 42, 43, 42, 42, 42, 42, 42, 44, 49, 50, 49, 49, 54, 54, 56, 55, 55, 55, 57, 58
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OFFSET
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1,4
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LINKS
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FORMULA
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EXAMPLE
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a(1)=1 because between p=2 and 4 there is exactly one prime, 3.
a(10)=6 since six consecutive primes (31,37,41,43,47,53) are located between p(10) = 29 and 58.
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MAPLE
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N:= 1000: # to get a(n) for n <= pi(N)
Primes:=select(isprime, [$1..N]):
seq(numtheory:-pi(2*Primes[n])-n, n=1..nops(Primes)); # Robert Israel, Aug 28 2014
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MATHEMATICA
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pp[n_]:=Module[{pr=Prime[n]}, PrimePi[2pr]-n]; Array[pp, 80] (* Harvey P. Dale, Mar 30 2015; edited by Zak Seidov, Oct 18 2022 *)
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PROG
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(PARI) forprime(p=2, 5000, n=0; for(q=p+1, 2*p-1, if(isprime(q), n++)); print1(n, ", ")) \\ Harry J. Smith, Dec 13 2007, improved by Colin Barker, Aug 28 2014
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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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EXTENSIONS
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STATUS
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approved
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