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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 16 03:55 EST 2019. Contains 319184 sequences. (Running on oeis4.)