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A016631 Decimal expansion of log(8). 13
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.
Bruce C. Berndt, Ramanujan's Notebooks Part I, Springer-Verlag.
LINKS
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.
FORMULA
Equals 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
Equals 2 + Sum_{n >= 1} (-1)^n*(n-1)/(n*(n+1)). - Bruno Berselli, Sep 09 2020
Equals 2 + Sum_{k>=1} zeta(2*k+1)/16^k. - Amiram Eldar, May 27 2021
Equals 3*A002162. - R. J. Mathar, Apr 11 2024
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
KEYWORD
nonn,cons,changed
AUTHOR
STATUS
approved

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Last modified April 14 03:49 EDT 2024. Contains 371655 sequences. (Running on oeis4.)