A100343 Denominators of the convergents in the continued fraction expansion for twice the constant given by A100338, where the partial quotients equal A006519 (greatest power of 2 dividing n) interleaved with 2's.

1, 1, 3, 7, 17, 24, 65, 284, 633, 917, 2467, 5851, 14169, 20020, 54209, 453692, 961593, 1415285, 3792163, 8999611, 21791385, 30790996, 83373377, 364284504, 811942385, 1176226889, 3164396163, 7505019215, 18174434593, 25679453808, 69533342209

Offset

1,3

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..31.

Formula

a(1) = 1, a(2) = 1; a(2*n) = a(2*n-1)*A006519(n) + a(2*n-2) for n>1, a(2*n-1) = 2*a(2*n-2) + a(2*n-3) for n>1.

Example

The constant is 2*x=2.707742256859764748777788168033216248454666833624237..
contfrac(2*x) = [2;1, 2,2, 2,1, 2,4, 2,1, 2,2, 2,1, 2,8,... 2, A006519(n),... ].

Prog

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

Crossrefs

Cf. A100338, A006519, A100340, A100341, A100342.

Sequence in context: A079470 A056815 A127176 * A085396 A041077 A041663

Adjacent sequences: A100340 A100341 A100342 * A100344 A100345 A100346

Keyword

cofr,nonn

Author

Paul D. Hanna, Nov 18 2004

Status

approved