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

Author

Paul D. Hanna, Nov 18 2004

Keywords

• cofr
• nonn

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.

Examples

			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),... ].
		

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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