A059445 Continued fraction for square root of (Pi * e / 2).

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, 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, 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

Offset: 0

Author

Robert G. Wilson v, Feb 01 2001

Keywords

• cofr
• nonn

Examples

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

References

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

Links

• Harry J. Smith, Table of n, a(n) for n = 0..19999
• C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review

Crossrefs

Cf. A059444 (decimal expansion).

Programs

Mathematica

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

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

Extensions

Offset changed by Andrew Howroyd, Aug 04 2024