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A100341
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).
4
1, 2, 3, 14, 17, 48, 65, 568, 633, 1834, 2467, 11702, 14169, 40040, 54209, 907384, 961593, 2830570, 3792163, 17999222, 21791385, 61581992, 83373377, 728569008, 811942385, 2352453778, 3164396163, 15010038430, 18174434593, 51358907616
OFFSET
1,2
COMMENTS
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.
FORMULA
a(1) = 1, a(2) = 2, a(n) = a(n-1)*A006519(n) + a(n-2).
EXAMPLE
The constant is x=1.353871128429882374388894084016608124227333416812...
contfrac(x) = [1;2,1,4,1,2,1,8,1,2,1,4,1,2,1,16,...A006519(n),... ].
PROG
(PARI) a(n)=if(n==1, 1, if(n==2, 2, a(n-1)*2^valuation(n, 2)+a(n-2)))
CROSSREFS
KEYWORD
cofr,nonn
AUTHOR
Paul D. Hanna, Nov 18 2004
STATUS
approved