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A053510
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Decimal expansion of log(Pi).
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41
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1, 1, 4, 4, 7, 2, 9, 8, 8, 5, 8, 4, 9, 4, 0, 0, 1, 7, 4, 1, 4, 3, 4, 2, 7, 3, 5, 1, 3, 5, 3, 0, 5, 8, 7, 1, 1, 6, 4, 7, 2, 9, 4, 8, 1, 2, 9, 1, 5, 3, 1, 1, 5, 7, 1, 5, 1, 3, 6, 2, 3, 0, 7, 1, 4, 7, 2, 1, 3, 7, 7, 6, 9, 8, 8, 4, 8, 2, 6, 0, 7, 9, 7, 8, 3, 6, 2, 3, 2, 7, 0, 2, 7, 5, 4, 8, 9, 7, 0, 7, 7, 0, 2, 0, 0, 9
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OFFSET
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1,3
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COMMENTS
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Also the least positive x such that sin(exp(x))==0.
Cheng, Dietel, Herblot, Huang, Krieger, Marques, Mason, Mereb, & Wilson show, expanding a remark by S. Lang, that Schanuel's conjecture implies that this constant and Pi are algebraically independent over a set E which includes the algebraic numbers and (in a technical sense) allows any finite number of exponentiations, see the paper for details and a still more general result. - Charles R Greathouse IV, Dec 15 2019
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REFERENCES
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Wolfram Research, 1991 Mathematica Conference, Elementary Tutorial Notes, Section 1, Introduction to Mathematica, Paul Abbott, page 25.
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LINKS
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Chuangxun Cheng, Brian Dietel, Mathilde Herblot, Jingjing Huang, Holly Krieger, Diego Marques, Jonathan Mason, Martin Mereb, S. Robert Wilson, Some consequences of Schanuel's conjecture, Journal of Number Theory 129:6 (2009), pp. 1464-1467.
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FORMULA
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Equals 1 + Sum_{n>=1} zeta(2*n)/(n*(2*n+1)*2^(2*n)), where zeta is the Riemann zeta function. - Vaclav Kotesovec, Mar 04 2016
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EXAMPLE
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1.1447298858494001741...
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MATHEMATICA
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RealDigits[Log[Pi], 10, 111][[1]]
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PROG
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(Magma) R:= RealField(100); Log(Pi(R)); // G. C. Greubel, May 15 2019
(SageMath) numerical_approx(log(pi), digits=100) # G. C. Greubel, May 15 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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Hsu, Po-Wei (Benny) (arsene_lupin(AT)intekom.co.za), Jan 14 2000
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EXTENSIONS
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STATUS
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approved
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