A100340 Numerators 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, 3, 4, 19, 23, 65, 88, 769, 857, 2483, 3340, 15843, 19183, 54209, 73392, 1228481, 1301873, 3832227, 5134100, 24368627, 29502727, 83374081, 112876808, 986388545, 1099265353, 3184919251, 4284184604, 20321657667, 24605842271, 69533342209

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) = 3, 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),... ].

Mathematica

Convergents[ Array[ 2^IntegerExponent[#, 2]&, 30] ] // Numerator (* Jean-François Alcover, May 15 2014 *)

Prog

(PARI) a(n)=if(n==1, 1, if(n==2, 3, a(n-1)*2^valuation(n, 2)+a(n-2)))

Crossrefs

Cf. A100338, A006519, A100341, A100342, A100343.

Sequence in context: A348349 A248590 A143150 * A042175 A041703 A036253

Adjacent sequences: A100337 A100338 A100339 * A100341 A100342 A100343

Keyword

cofr,nonn

Author

Paul D. Hanna, Nov 18 2004

Status

approved