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A060208
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2Pi(n) - Pi(2n), where Pi is A000720.
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5
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-1, 0, 1, 0, 2, 1, 2, 2, 1, 0, 2, 1, 3, 3, 2, 1, 3, 3, 4, 4, 3, 2, 4, 3, 3, 3, 2, 2, 4, 3, 4, 4, 4, 3, 3, 2, 3, 3, 3, 2, 4, 3, 5, 5, 4, 4, 6, 6, 5, 5, 4, 3, 5, 4, 3, 3, 2, 2, 4, 4, 6, 6, 6, 5, 5, 4, 6, 6, 5, 4, 6, 6, 8, 8, 7, 6, 6, 6, 7, 7, 7, 6, 8, 7, 7, 7, 6, 6, 8, 7, 6, 6, 6, 6, 6, 5, 6, 6, 5, 4, 6, 6, 8, 8, 8, 7, 9, 9, 11, 11, 11, 10, 12, 11, 10, 10, 9, 9, 9, 8, 7, 7
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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REFERENCES
| S. Segal, On Pi(x+1)<=Pi(x)+Pi(y). Transactions American Mathematical Society, 104 (1962), 523-527.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
E. Labos, Illustration
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FORMULA
| a(n) = Mod[2*PrimePi[n], PrimePi[2n]] = 2*A000720(n)-A000720(2n) for n>1.
a(n) ~ 2n log 2 / (log n)^2, by the prime number theorem. - N. J. A. Sloane (njas(AT)research.att.com), Mar 12 2007
a(n) = -A047886(n,n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 15 2008
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EXAMPLE
| n=100, Pi(100)=25, Pi(200)=46, 2*Pi(100)-Pi(2*100) =4=a(100)
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MATHEMATICA
| f[n_] := 2 PrimePi[n] - PrimePi[2 n]; Array[f, 122] (* Robert G. Wilson v, Aug 12, 2011 *)
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CROSSREFS
| Cf. A060207, A007097, A000720, A033844.
Sequence in context: A127249 A127251 A063251 * A004570 A178064 A145363
Adjacent sequences: A060205 A060206 A060207 * A060209 A060210 A060211
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KEYWORD
| sign
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Mar 19 2001
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