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A229989
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Number of primes in the interval [floor(n/2), floor(3n/2)].
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2
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0, 2, 2, 3, 4, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 7, 7, 7, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 13, 14, 14, 14, 15, 16, 16, 16, 17, 18, 18, 18
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OFFSET
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1,2
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COMMENTS
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Conjectures:
(1) a(n+1) - a(n) = 1 for infinitely many n;
(2) a(n+1) - a(n) = -1 for infinitely many n;
(3) a(n+1) - a(n) = -1 if and only if n = 2*prime(m+1) - 1.
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LINKS
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EXAMPLE
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a(5) = 4 counts the primes in the interval [2,7].
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MAPLE
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MATHEMATICA
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z = 1000; c[n_] := PrimePi[Floor[3 n/2]] - PrimePi[Floor[n/2]-1];
t = Table[c[n], {n, 1, z}]; (* A229989 *)
Flatten[Position[Differences[t], -1]] (* A076274? *)
Flatten[Position[Differences[t], 1]] (* A229990 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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