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Denominators of the convergents in the continued fraction expansion for the constant given by A100338, where the partial quotients equal A006519 (greatest power of 2 dividing n).
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%I #5 Mar 30 2012 18:36:44

%S 1,2,3,14,17,48,65,568,633,1834,2467,11702,14169,40040,54209,907384,

%T 961593,2830570,3792163,17999222,21791385,61581992,83373377,728569008,

%U 811942385,2352453778,3164396163,15010038430,18174434593,51358907616

%N Denominators of the convergents in the continued fraction expansion for the constant given by A100338, where the partial quotients equal A006519 (greatest power of 2 dividing n).

%C The convergents for the continued fraction of x are given by A100340(n)/A100341(n) and the convergents for the continued fraction of 2*x are given by A100342(n)/A100343(n), where A100342(n)/A100343(n) = 2*A100340(n)/A100341(n) for all n.

%F a(1) = 1, a(2) = 2, a(n) = a(n-1)*A006519(n) + a(n-2).

%e The constant is x=1.353871128429882374388894084016608124227333416812...

%e contfrac(x) = [1;2,1,4,1,2,1,8,1,2,1,4,1,2,1,16,...A006519(n),... ].

%o (PARI) a(n)=if(n==1,1,if(n==2,2,a(n-1)*2^valuation(n,2)+a(n-2)))

%Y Cf. A100338, A006519, A100340, A100342, A100343.

%K cofr,nonn

%O 1,2

%A _Paul D. Hanna_, Nov 18 2004