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Continued fraction for square root of (Pi * e / 2).
2

%I #18 Aug 04 2024 12:44:55

%S 2,15,14,1,2,3,17,1,1,5,1,30,1,3,2,1,1,1,3,3,1,4,2,9,2,1,9,1,7,1,6,1,

%T 5,1,5,3,1,1,3,1,36,4,18,2,1,2,4,1,3,366,3,1,1,16,2,1,2,2,1,3,3,1,5,2,

%U 2,34,1,2,2,1,18,1,1,16,1,1,1,3,4,7,1,21,6,5,1,2,1,11,4,1,1,14,4,17,1,1

%N Continued fraction for square root of (Pi * e / 2).

%D C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Oxford University Press, Oxford and NY, 2001, page 68.

%H Harry J. Smith, <a href="/A059445/b059445.txt">Table of n, a(n) for n = 0..19999</a>

%H C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," <a href="http://www.zentralblatt-math.org/zmath/en/search/?q=an:0983.00008&amp;format=complete">Zentralblatt review</a>

%e 2.0663656770612464692346959... = 2 + 1/(15 + 1/(14 + 1/(1 + 1/(2 + ...)))). - _Harry J. Smith_, Jun 27 2009

%t ContinuedFraction[Sqrt[ \[Pi]*\[ExponentialE]/2], 100]

%o (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(sqrt(Pi*exp(1)/2)); for (n=1, 20000, write("b059445.txt", n-1, " ", x[n])); } \\ _Harry J. Smith_, Jun 27 2009

%Y Cf. A059444 (decimal expansion).

%K cofr,nonn

%O 0,1

%A _Robert G. Wilson v_, Feb 01 2001

%E Offset changed by _Andrew Howroyd_, Aug 04 2024