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A002390
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Decimal expansion of natural logarithm of golden ratio.
(Formerly M3318 N1334)
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21
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4, 8, 1, 2, 1, 1, 8, 2, 5, 0, 5, 9, 6, 0, 3, 4, 4, 7, 4, 9, 7, 7, 5, 8, 9, 1, 3, 4, 2, 4, 3, 6, 8, 4, 2, 3, 1, 3, 5, 1, 8, 4, 3, 3, 4, 3, 8, 5, 6, 6, 0, 5, 1, 9, 6, 6, 1, 0, 1, 8, 1, 6, 8, 8, 4, 0, 1, 6, 3, 8, 6, 7, 6, 0, 8, 2, 2, 1, 7, 7, 4, 4, 1, 2, 0, 0, 9, 4, 2, 9, 1, 2, 2, 7, 2, 3, 4, 7, 4
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Also equals asinh(1/2).
Equals sqrt(5)/2 * Sum_{n=1..infinity} (-1)^(n-1)/(n*C(2*n,n)). - Seiichi Kirikami, Aug 20 2011
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REFERENCES
| W. E. Mansell, Tables of Natural and Common Logarithms. Royal Society Mathematical Tables, Vol. 8, Cambridge Univ. Press, 1964, p. XVIII.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| S. Plouffe, Plouffe's Inverter, ln(phi) to 10000 digits
S. Plouffe, ln(0.5+0.5*SQRT(5)) to 2000 digits
Eric Weisstein's World of Mathematics, Fibonacci Hyperbolic Functions
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EXAMPLE
| .48121182505960344749775891342436842313518433438566051966101...
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MAPLE
| arcsinh(1/2);
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MATHEMATICA
| RealDigits[N[Log[GoldenRatio], 200]][[1]] (*From Vladimir Joseph Stephan Orlovsky, Feb 20 2011*)
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CROSSREFS
| Cf. A001622.
Sequence in context: A200356 A127734 A154520 * A193087 A201404 A122149
Adjacent sequences: A002387 A002388 A002389 * A002391 A002392 A002393
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KEYWORD
| nonn,cons
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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