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A016631 Decimal expansion of log(8). 5
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.

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.

Eugen J. Ionascu and Gabriel Prajitura, Things to do with a broken stick,  arXiv:1009.0890v1 [math.HO]

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].

EXAMPLE

2.079441541679835928251696364374529704226500403080765762362040028480180... [Harry J. Smith, May 16 2009]

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:

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)); } [From Harry J. Smith, May 16 2009]

CROSSREFS

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

Sequence in context: A011389 A021485 A019821 * A164269 A121814 A195298

Adjacent sequences:  A016628 A016629 A016630 * A016632 A016633 A016634

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Fixed my PARI program, had -n Harry J. Smith, May 19 2009

Gave another definition of the sequence in terms of a geometric probability and added a Maple code to compute it.

STATUS

approved

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Last modified October 20 21:27 EDT 2014. Contains 248371 sequences.