|
| |
|
|
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; 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.
|
|
|
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 (pauldhanna(AT)juno.com), Nov 18 2004
|
| |
|
|
