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A062542
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Decimal expansion of the continued fraction constant (base 10).
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1
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1, 0, 3, 0, 6, 4, 0, 8, 3, 4, 1, 0, 0, 7, 1, 2, 9, 3, 5, 8, 8, 1, 7, 7, 6, 0, 9, 4, 1, 1, 6, 9, 3, 6, 8, 4, 0, 9, 2, 5, 9, 2, 0, 3, 1, 1, 1, 2, 0, 7, 2, 6, 2, 8, 1, 7, 7, 0, 0, 6, 0, 9, 5, 2, 2, 3, 4, 9, 5, 4, 4, 2, 8, 0, 0, 4, 7, 9, 9, 7, 6, 7, 5, 1, 8, 3, 6, 0, 8, 0, 8, 3, 9, 5, 6, 5, 8, 6, 5, 4, 7, 6, 2, 6, 3
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OFFSET
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1,3
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COMMENTS
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"(By strange coincidence, the information in a typical continued fraction term is very nearly one decimal digit - actually pi^2/(6 (ln 2) (ln 10)) = 1.0306.) R. W. Gosper. Math-Fun list, April 9, 1998. This constant is the average number of decimal digits necessary to have the equivalent continued fraction representations of a number in base 10. In other words if you have N decimal digits it will give you N/C = N/1.0306 valid partial quotients in average." - Simon Plouffe.
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LINKS
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Table of n, a(n) for n=1..105.
_Simon Plouffe_, Plouffe's Inverter
Eric Weisstein's World of Mathematics, Lochs' Theorem
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FORMULA
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pi^2/(6 (ln 2) (ln 10)).
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EXAMPLE
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1.03064083410071293588177609411693684092592031112072628177006095223495442800479...
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MATHEMATICA
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RealDigits[Pi^2/(6Log[2]Log[10]), 10, 120][[1]] (* From Harvey P. Dale, Apr 11 2012 *)
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CROSSREFS
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Cf. A062543.
Sequence in context: A215664 A088162 A133170 * A109693 A188858 A199610
Adjacent sequences: A062539 A062540 A062541 * A062543 A062544 A062545
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KEYWORD
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cons,easy,nonn
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AUTHOR
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Jason Earls (zevi_35711(AT)yahoo.com), Jun 25 2001
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STATUS
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approved
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