%I #16 Aug 04 2024 11:41:34

%S 5,1,6,7,3,21,2,1,2,2,1,1,2,3,3,2,5,2,1,1,1,1,3,1,8,4,4,1,1,1,1,8,1,4,

%T 1,5,1,1,1,2,4,3,2,1,1,2,1,10,1,4,1,2,1,12,1,8,2,7,39,365,2,15,2,25,1,

%U 2,5,3,3,9,3,1,1,9,1,1,47,1,1,18,1,1,2,6,1,1,1,4,1,3,1,1,1,1,4,1,6,37

%N Continued fraction for Pi + e.

%C The question of the transcendence of the number Pi + e is still open.

%H Harry J. Smith, <a href="/A058651/b058651.txt">Table of n, a(n) for n = 0..19999</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 a(1) = 5 because Pi + e = 5.859874482048838473822930854632165381954416493075065395941912220031...

%e 5.859874482048838473822930854... = 5 + 1/(1 + 1/(6 + 1/(7 + 1/(3 + ...)))). - _Harry J. Smith_, May 31 2009

%o (PARI) \p 500; contfrac(Pi+exp(1))

%o (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(Pi+exp(1)); for (n=1, 20000, write("b058651.txt", n-1, " ", x[n])); } \\ _Harry J. Smith_, May 31 2009

%Y Cf. A001203, A003417.

%Y Cf. A059742 (decimal expansion).

%K nonn,cofr,easy

%O 0,1

%A Avi Peretz (njk(AT)netvision.net.il), Dec 26 2000

%E More terms from _Jason Earls_, Jun 28 2001

%E Offset changed by _Andrew Howroyd_, Aug 04 2024