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A106313
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Differences between the prime-counting function and Gauss' approximation.
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1
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1, 4, 9, 16, 37, 129, 338, 753, 1700, 3103, 11587, 38262, 108970, 314889, 1052618, 3214631, 7956588, 21949554, 99877774, 222744643, 597394253, 1932355207, 7250186215, 17146907277
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| Jonathan Borwein, David H. Bailey, "Mathematics by Experiment", A. K. Peters, 2004, p. 65 (Table 2.2).
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FORMULA
| The prime counting function Pi(x) runs through x = 10^1, 10^2, 10^3...; being subtracted from Gauss' approximation, integral(2, x)dt/log t.
a(n) = A190802(n) - A006880(n).
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EXAMPLE
| Given x = 10^4, Pi(x) = 1229, Gauss' approximation = 1245. Thus a(4) = 1245 - 1229 = 16.
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CROSSREFS
| Sequence in context: A138858 A076967 A111378 * A074101 A034377 A034378
Adjacent sequences: A106310 A106311 A106312 * A106314 A106315 A106316
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 28 2005
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EXTENSIONS
| a(23)-a(24) from Nathaniel Johnston (nathaniel(AT)nathanieljohnston.com), May 25 2011
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