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

0,5

Links

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

Example

1.646760258121065648366051222... = 1 + 1/(1 + 1/(1 + 1/(1 + 1/(4 + ...)))). - Harry J. Smith, Oct 04 2009

Mathematica

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

Prog

(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

Crossrefs

Cf. A065445 (decimal expansion).

Sequence in context: A328302 A346748 A348184 * A185088 A064947 A369894

Adjacent sequences: A065042 A065043 A065044 * A065046 A065047 A065048

Keyword

cofr,nonn

Author

Robert G. Wilson v, Nov 19 2001

Extensions

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

Offset changed by Andrew Howroyd, Aug 05 2024

Status

approved