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%I #12 Jan 03 2016 03:46:07
%S 1,1,5,1,3,15,1,5,3,2,7,2,1,62,1,3,110,1,39,1,1,1,4,3,1,2,5,2,2,28,1,
%T 1,1,2,6,2,2,1,278,3,3,1,1,4,1,4,2,5,5,2,4,1,1,1,28,1,1,203,1,89,2,2,
%U 2,1,12,1,1,3,33,1,8,3,1,2,6,1,1,3,256,1,6,5,1,6,14,1
%N Continued fraction for Integral_{x=0..Pi} sin(x)/x.
%C Integral(sin(x)/x dx) = x - x^3/(3*3!) + x^5/(5*5!) - x^7/(7*7!) + ... - _Harry J. Smith_, May 01 2009
%H Harry J. Smith, <a href="/A036790/b036790.txt">Table of n, a(n) for n = 1..20000</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 1.851937051982466170361053370... = 1 + 1/(1 + 1/(5 + 1/(1 + 1/(3 + ...)))). - _Harry J. Smith_, May 01 2009
%o (PARI) { allocatemem(932245000); default(realprecision, 21000); y=0; x=Pi; m=x; x2=x*x; n=1; nf=1; s=1; while (x!=y, y=x; n++; nf*=n; n++; nf*=n; m*=x2; s=-s; x+=s*m/(n*nf)); x=contfrac(x); for (n=1, 20000, write("b036790.txt", n, " ", x[n])); } \\ _Harry J. Smith_, May 01 2009
%Y Cf. A036792.
%K nonn,cofr
%O 1,3
%A _N. J. A. Sloane_
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