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

1,5

Links

Harry J. Smith, Table of n, a(n) for n = 1..2000

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, " ", x[n])) } \\ Harry J. Smith, Oct 04 2009

Crossrefs

Cf. A065445.

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

Status

approved