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A016631 Decimal expansion of log(8). 6
2, 0, 7, 9, 4, 4, 1, 5, 4, 1, 6, 7, 9, 8, 3, 5, 9, 2, 8, 2, 5, 1, 6, 9, 6, 3, 6, 4, 3, 7, 4, 5, 2, 9, 7, 0, 4, 2, 2, 6, 5, 0, 0, 4, 0, 3, 0, 8, 0, 7, 6, 5, 7, 6, 2, 3, 6, 2, 0, 4, 0, 0, 2, 8, 4, 8, 0, 1, 8, 0, 8, 6, 5, 9, 0, 9, 0, 8, 4, 1, 4, 6, 8, 1, 7, 5, 8, 9, 9, 8, 0, 9, 8, 9, 2, 5, 6, 0, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n+1) is also the sequence of digits in the base-ten expansion of the number representing the probability that an acute triangle could be formed with the pieces obtained by breaking a stick into three parts at random. The breaking points are chosen with uniform distribution and independently of one another. - Eugen J. Ionascu, Feb 19 2011

REFERENCES

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 2.

B. C. Berndt, Ramanujan's Notebooks Part I, Springer-Verlag.

LINKS

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].

Eugen J. Ionascu and Gabriel Prajitura, Things to do with a broken stick, arXiv:1009.0890 [math.HO], 2010-2013.

Index entries for transcendental numbers

FORMULA

Log(8) = 2 + Sum_{n >= 1} 1/( n*(16*n^2 - 1) ). This summation was the first problem submitted by Ramanujan to the Journal of the Indian Mathematical Society. See Berndt, Corollary on p. 29. - Peter Bala, Feb 25 2015

Log(8) = 2 + Sum_{n >= 1} (-1)^n*(n-1)/(n*(n+1)). - Bruno Berselli, Sep 09 2020

EXAMPLE

2.079441541679835928251696364374529704226500403080765762362040028480180....

MAPLE

a:=proc(n)

  local x, y, z, w;

    Digits:=2*n+1;

     x:=3*ln(2); y:=floor(10^(n-2)*x)*10;

       z:=floor(10^(n-1)*x); w:=z-y;

end: # Eugen J. Ionascu, Feb 19 2011

MATHEMATICA

RealDigits[Log[8], 10, 90][[1]] (* Bruno Berselli, Mar 26 2013 *)

PROG

(PARI) default(realprecision, 20080); x=log(8); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b016631.txt", n, " ", d)); \\ Harry J. Smith, May 16 2009

CROSSREFS

Cf. A016736 (continued fraction). - Harry J. Smith, May 16 2009

Sequence in context: A011389 A021485 A019821 * A164269 A293265 A121814

Adjacent sequences:  A016628 A016629 A016630 * A016632 A016633 A016634

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 25 05:43 EST 2020. Contains 338617 sequences. (Running on oeis4.)