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A109168
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Continued fraction expansion of constant x (A109169) such that the continued fraction of 2*x yields the continued fraction of x interleaved with positive even numbers.
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4
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1, 2, 2, 4, 3, 4, 4, 8, 5, 6, 6, 8, 7, 8, 8, 16, 9, 10, 10, 12, 11, 12, 12, 16, 13, 14, 14, 16, 15, 16, 16, 32, 17, 18, 18, 20, 19, 20, 20, 24, 21, 22, 22, 24, 23, 24, 24, 32, 25, 26, 26, 28, 27, 28, 28, 32, 29, 30, 30, 32, 31, 32, 32, 64, 33, 34, 34, 36, 35, 36, 36, 40, 37, 38, 38
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Compare with continued fraction A100338.
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FORMULA
| For n>=1: a(2*n-1) = n, a(2*n) = 2*a(n).
a((2*n-1)*2^p) = n * 2^p, p>=0. [Johannes W. Meijer, Jun 22 2011]
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EXAMPLE
| x=1.408494279228906985748474279080697991613998955782051281466263817524862977...
The continued fraction expansion of 2*x = A109170:
[2;1, 4,2, 6,2, 8,4, 10,3, 12,4, 14,4, 16,8, 18,5, ...]
which equals the continued fraction of x interleaved with even numbers.
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MAPLE
| nmax:=75; pmax:= ceil(log(nmax)/log(2)); for p from 0 to pmax do for n from 1 to nmax do a((2*n-1)*2^p):= n*2^p: od: od: seq(a(n), n=1..nmax); [Johannes W. Meijer, Jun 22 2011]
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PROG
| (PARI) a(n)=if(n%2==1, (n+1)/2, 2*a(n/2))
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CROSSREFS
| Cf. A109169 (digits of x), A109170 (continued fraction of 2*x), A109171 (digits of 2*x).
Cf. A006519 and A129760. [Johannes W. Meijer, Jun 22 2011]
Sequence in context: A086835 A046701 A140472 * A015134 A171580 A177235
Adjacent sequences: A109165 A109166 A109167 * A109169 A109170 A109171
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KEYWORD
| cofr,nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jun 21 2005
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