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 A006085 Continued fraction for e/4. (Formerly M1822) 4

%I M1822

%S 0,1,2,8,3,1,1,1,1,7,1,1,2,1,1,1,2,7,1,2,2,1,1,1,3,7,1,3,2,1,1,1,4,7,

%T 1,4,2,1,1,1,5,7,1,5,2,1,1,1,6,7,1,6,2,1,1,1,7,7,1,7,2,1,1,1,8,7,1,8,

%U 2,1,1,1,9,7,1,9,2,1,1,1,10,7,1,10,2,1,1,1,11,7,1,11,2,1,1,1,12,7,1,12,2,1

%N Continued fraction for e/4.

%D D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 2, p. 601.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Harry J. Smith, <a href="/A006085/b006085.txt">Table of n, a(n) for n=1,...,20000</a>

%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>

%F First seven terms are 0, 1, 2, 8, 3, 1, 1; then a(8k)=1, a(8k+1)=k, a(8k+2)=7, a(8k+3)=1, a(8k+4)=k, a(8k+5)=2, a(8k+6)=1, a(8k+7)=1. - _Benoit Cloitre_, Apr 08 2003

%e 0.679570457114761308840071867... = 0 + 1/(1 + 1/(2 + 1/(8 + 1/(3 + ...)))) [From _Harry J. Smith_, May 10 2009]

%t ContinuedFraction[E/4,120] (* From Harvey P. Dale, Apr 01 2011 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 40000); x=contfrac(exp(1)/4); for (n=1, 20000, write("b006085.txt", n, " ", x[n])); } [From _Harry J. Smith_, May 10 2009]

%Y Cf. A019741 = Decimal expansion. [From _Harry J. Smith_, May 10 2009]

%K nonn,cofr,easy

%O 1,3

%A _N. J. A. Sloane_.

%E More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 20 2003

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