A100342 Numerators 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.

2, 3, 8, 19, 46, 65, 176, 769, 1714, 2483, 6680, 15843, 38366, 54209, 146784, 1228481, 2603746, 3832227, 10268200, 24368627, 59005454, 83374081, 225753616, 986388545, 2198530706, 3184919251, 8568369208, 20321657667, 49211684542

Offset

1,1

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..29.

Formula

a(1) = 2, a(2) = 3; 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, 2, if(n==2, 3, 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, A100343.

Sequence in context: A002356 A166302 A347736 * A041281 A078343 A378411

Adjacent sequences: A100339 A100340 A100341 * A100343 A100344 A100345

Keyword

cofr,nonn

Author

Paul D. Hanna, Nov 18 2004

Status

approved