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A055972 Continued fraction for the number 1 + 1/(e + 1/(e^2 + 1/(e^3 + 1/(e^4 +...)))). 2

%I

%S 1,2,1,5,1,3,1,2,1,57,1,5,3,1,2847,7,1,1,3,4,4,8,1,1,48,1,1,2,1,2,81,

%T 1,2,3,12,1,1,1,5,1,3,1,6,1,5,3,2,1,2,1,3,1,2,1,1,5,6,96,1,1,1,1,1,3,

%U 1,19

%N Continued fraction for the number 1 + 1/(e + 1/(e^2 + 1/(e^3 + 1/(e^4 +...)))).

%H Harry J. Smith, <a href="/A055972/b055972.txt">Table of n, a(n) for n = 0..2000</a>

%H G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>

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

%e 1.3505436043221124180470983246597483686...

%e 1.350543604322112418047098324... = 1 + 1/(2 + 1/(1 + 1/(5 + 1/(1 + ...)))). - _Harry J. Smith_, May 03 2009

%o (PARI) f(n)= { x=0; for (i=1, n, x=1/(exp(1+n-i) + x)); 1+x } { allocatemem(932245000); default(realprecision, 2100); y=1.0; n=70; x=f(n); while(x!=y, y=x; n=n+1; x=f(n);); c=contfrac(x); for (n=1, 2001, write("b055972.txt", n-1, " ", c[n])); } \\ _Harry J. Smith_, May 03 2009

%Y Cf. A100609 Decimal expansion. - _Harry J. Smith_, May 03 2009

%K cofr,nonn

%O 0,2

%A _Leroy Quet_, Jul 19 2000

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Last modified March 26 19:03 EDT 2019. Contains 321511 sequences. (Running on oeis4.)