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%I #14 Aug 05 2024 12:46:08
%S 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,
%T 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,
%U 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
%N Continued fraction expansion of the constant Product_{k>=0} (1 + 1/2^(2k))^(1/2) (A065445).
%H Harry J. Smith, <a href="/A065045/b065045.txt">Table of n, a(n) for n = 0..1999</a>
%e 1.646760258121065648366051222... = 1 + 1/(1 + 1/(1 + 1/(1 + 1/(4 + ...)))). - _Harry J. Smith_, Oct 04 2009
%t ContinuedFraction[ N[ Product[ Sqrt[ (1 + 1/2^(2k) ) ], {k, 0, Infinity} ], 500 ], 100 ]
%o (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
%Y Cf. A065445 (decimal expansion).
%K cofr,nonn
%O 0,5
%A _Robert G. Wilson v_, Nov 19 2001
%E Terms corrected and terms added by _Harry J. Smith_, Oct 04 2009
%E Offset changed by _Andrew Howroyd_, Aug 05 2024