A065045 Continued fraction expansion of the constant Product_{k>=0} (1 + 1/2^(2k))^(1/2) (A065445).

1, 1, 1, 1, 4, 1, 10, 1, 3, 3, 1, 2, 10, 1, 1, 1, 13, 1, 18, 1, 1, 2, 16, 1, 223, 1, 2, 3, 2, 6, 56, 1, 3, 5, 3, 14, 1, 8, 1, 1, 8, 135, 8, 1, 1, 2, 6, 1, 3, 2, 5, 6, 3, 1, 2, 1, 12, 1, 1, 72, 2, 2, 1, 4, 1, 10, 1, 2, 14, 1, 2, 1, 1, 2, 6, 2, 10, 9, 47, 1, 9, 3, 3, 1, 2, 5, 2, 1, 5, 1, 1, 3, 15, 1, 2, 2, 8

Offset: 0

Author

Robert G. Wilson v, Nov 19 2001

Keywords

• cofr
• nonn

Examples

			1.646760258121065648366051222... = 1 + 1/(1 + 1/(1 + 1/(1 + 1/(4 + ...)))). - _Harry J. Smith_, Oct 04 2009
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..1999

Crossrefs

Cf. A065445 (decimal expansion).

Programs

Mathematica

ContinuedFraction[ N[ Product[ Sqrt[ (1 + 1/2^(2k) ) ], {k, 0, Infinity} ], 500 ], 100 ]

PARI

{ allocatemem(932245000); default(realprecision, 2300); x=contfrac(prodinf(k=0, sqrt(1 + 1/2^(2*k)))); for (n=1, 2000, write("b065045.txt", n-1, " ", x[n])) } \\ Harry J. Smith, Oct 04 2009

Extensions

Terms corrected and terms added by Harry J. Smith, Oct 04 2009

Offset changed by Andrew Howroyd, Aug 05 2024