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).

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.

Links

Table of n, a(n) for n=1..30.

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

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

Sequence in context: A281500 A041009 A042367 * A041869 A041010 A041733

Adjacent sequences: A100338 A100339 A100340 * A100342 A100343 A100344

Keyword

cofr,nonn

Author

Paul D. Hanna, Nov 18 2004

Status

approved