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A016628
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Decimal expansion of log(5).
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11
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1, 6, 0, 9, 4, 3, 7, 9, 1, 2, 4, 3, 4, 1, 0, 0, 3, 7, 4, 6, 0, 0, 7, 5, 9, 3, 3, 3, 2, 2, 6, 1, 8, 7, 6, 3, 9, 5, 2, 5, 6, 0, 1, 3, 5, 4, 2, 6, 8, 5, 1, 7, 7, 2, 1, 9, 1, 2, 6, 4, 7, 8, 9, 1, 4, 7, 4, 1, 7, 8, 9, 8, 7, 7, 0, 7, 6, 5, 7, 7, 6, 4, 6, 3, 0, 1, 3, 3, 8, 7, 8, 0, 9, 3, 1, 7, 9, 6, 1
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OFFSET
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1,2
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REFERENCES
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Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 2.
Horace S. Uhler, Recalculation and extension of the modulus and of the logarithms of 2, 3, 5, 7 and 17. Proc. Nat. Acad. Sci. U. S. A. 26, (1940). 205-212.
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LINKS
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Harry J. Smith, Table of n, a(n) for n = 1..20000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Simon Plouffe, The natural logarithm of 5 to 10000 digits
Index entries for transcendental numbers
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FORMULA
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From Peter Bala, Nov 11 2019: (Start)
log(5) = 2*sqrt(2)*Integral_{t = 0..sqrt(2)/2} (1 - t^2)/(1 + t^4) dt.
log(5) = Sum_{n >= 0} (4*n+5)/((4*n+1)*(4*n+3))*(-1/4)^n.
log(5) = (1/4)*Sum_{n >= 0} ( 8/(8*n+1) - 4/(8*n+3) - 2/(8*n+5) + 1/(8*n+7) )*(1/16)^n, a BBP-type formula. (End)
log(5) = 2*Sum_{n >= 0} (-1)^(n*(n+1)/2)*1/((2*n+1)*2^n). - Peter Bala, Oct 29 2020
log(5) = Integral_{x = 0..1} (x^4 - 1)/log(x) dx. - Peter Bala, Nov 14 2020
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EXAMPLE
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1.60943791243410037460075933322618763952560135426851772191264789... - Harry J. Smith, May 16 2009
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MATHEMATICA
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RealDigits[Log[5], 10, 125][[1]] (* Alonso del Arte, Oct 04 2014 *)
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PROG
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(PARI) default(realprecision, 20080); x=log(5); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b016628.txt", n, " ", d)); \\ Harry J. Smith, May 16 2009
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CROSSREFS
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Cf. A016733 (continued fraction). - Harry J. Smith, May 16 2009
Sequence in context: A323606 A133077 A200124 * A112246 A189037 A153201
Adjacent sequences: A016625 A016626 A016627 * A016629 A016630 A016631
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KEYWORD
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nonn,cons,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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