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A124478
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Let p(n) = prime(n); sequence gives p(n) - floor( (2/n)*(Sum_{i=1..n} p(i)) ).
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1
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-2, -2, -1, -1, 0, 0, 1, 0, 1, 4, 2, 5, 5, 3, 4, 6, 8, 6, 8, 8, 6, 8, 7, 9, 13, 12, 10, 10, 7, 7, 17, 16, 17, 14, 19, 17, 18, 19, 18, 19, 20, 17, 22, 19, 18, 16, 23, 29, 28, 25, 24, 25, 21, 26, 27, 28, 28, 25, 26, 25, 22, 27, 35, 34, 30, 29, 37, 38, 42, 38, 37, 37, 40, 40, 40, 39, 39, 41, 40, 42
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Robert Mandl conjectured and Rosser and Schoenfeld proved that p(n)/2 > (Sum_{i=1..n} p(i))/n for n >= 9 (implying that a(n) > 0 for n >= 9).
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REFERENCES
| Rosser, J. Barkley; and Schoenfeld, Lowell; Sharper bounds for the Chebyshev functions theta(x) and psi(x), Math. Comp. 29 (1975), 243-269.
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LINKS
| Zak Seidov, Table of n, a(n) for n = 1..1000.
Pierre Dusart, Autour de la fonction qui compte le nombre de nombres premiers, Th\`ese, Universit\'e de Limoges, France, (1998), see Section 1.9.
M. Hassani, A Remark on the Mandl's Inequality.
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CROSSREFS
| Sequence in context: A054924 A025485 A046751 * A030353 A089617 A128521
Adjacent sequences: A124475 A124476 A124477 * A124479 A124480 A124481
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KEYWORD
| sign
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 17 2006
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