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Search: id:A109170
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| A109170 |
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Continued fraction expansion of 2*x which equals the continued fraction of x (A109168) interleaved with positive even numbers. |
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+0
4
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| 2, 1, 4, 2, 6, 2, 8, 4, 10, 3, 12, 4, 14, 4, 16, 8, 18, 5, 20, 6, 22, 6, 24, 8, 26, 7, 28, 8, 30, 8, 32, 16, 34, 9, 36, 10, 38, 10, 40, 12, 42, 11, 44, 12, 46, 12, 48, 16, 50, 13, 52, 14, 54, 14, 56, 16, 58, 15, 60, 16, 62, 16, 64, 32, 66, 17, 68, 18, 70, 18, 72, 20, 74, 19, 76, 20, 78
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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For n>=1: a(2*n-1) = 2*n, a(4*n-2) = n, a(4*n) = 2*a(2*n).
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EXAMPLE
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2*x=2.8169885584578139714969485581613959832279979115641025629325276350497259...
The continued fraction expansion of x = A109168:
[1; 2, 2, 4, 3, 4, 4, 8, 5, 6, 6, 8, 7, 8, 8, 16, ...];
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), if(n%4==2, (n+2)/4, 2*a(n/2)))
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CROSSREFS
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Cf. A109168 (continued fraction of x), A109169 (digits of x), A109171 (digits of 2*x).
Sequence in context: A093819 A089929 A131888 this_sequence A099311 A130742 A130107
Adjacent sequences: A109167 A109168 A109169 this_sequence A109171 A109172 A109173
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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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