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Continued fraction for Pi/2.
7

%I #20 Sep 08 2022 08:45:00

%S 1,1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,1,5,1,41,1,2,3,7,1,1,1,27,1,1,

%T 1,2,1,2,1,1,2,1,1,49,2,1,4,3,6,2,1,3,3,17,1,3,2,1,6,3,1,6,26,3,1,1,3,

%U 4,3,2,14,11,1,4,1,1,5,2,8,8,2,80,1,1,22,2,11,2,1

%N Continued fraction for Pi/2.

%H Harry J. Smith, <a href="/A053300/b053300.txt">Table of n, a(n) for n = 0..20000</a>

%H Michael A. Filaseta, Allen Stenger, D. Callan and Z. Franco, <a href="http://www.jstor.org/stable/2589451">Solution to Problem 10640: When a Multiple of Pi/2 is Close to an Integer</a>, Amer. Math. Monthly, 107 (2000), 177-178.

%H I. Rosenholtz, <a href="http://www.jstor.org/stable/2690793">Tangent sequences, world records, ...</a>, Math. Mag., 72 (No. 5, 1999), 367-376.

%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 1.57079632679489661923132169... = 1 + 1/(1 + 1/(1 + 1/(3 + 1/(31 + ...)))). - _Harry J. Smith_, May 31 2009

%t ContinuedFraction[ Pi/2, 100 ]

%o (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(Pi/2); for (n=0, 20000, write("b053300.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, May 31 2009

%o (Magma) R:= RealField(); ContinuedFraction(Pi(R)/2); // _G. C. Greubel_, May 24 2018

%Y Cf. A001203.

%Y Cf. A019669 (decimal expansion). - _Harry J. Smith_, May 31 2009

%K nonn,cofr

%O 0,4

%A _N. J. A. Sloane_, Mar 21 2000