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Search: id:A109168
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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; listen)
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OFFSET
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1,2
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COMMENT
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Compare with continued fraction A100338.
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FORMULA
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For n>=1: a(2*n-1) = n, a(2*n) = 2*a(n).
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EXAMPLE
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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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PROGRAM
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(PARI) a(n)=if(n%2==1, (n+1)/2, 2*a(n/2))
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CROSSREFS
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Cf. A109169 (digits of x), A109170 (continued fraction of 2*x), A109171 (digits of 2*x).
Sequence in context: A086835 A046701 A140472 this_sequence A015134 A079707 A131816
Adjacent sequences: A109165 A109166 A109167 this_sequence A109169 A109170 A109171
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KEYWORD
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cofr,nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jun 21 2005
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