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Search: id:A109169
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| A109169 |
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Decimal expansion of constant x such that the continued fraction expansion of 2*x (A109170) yields the continued fraction expansion of x (A109168) interleaved with positive even numbers. |
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+0
4
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| 1, 4, 0, 8, 4, 9, 4, 2, 7, 9, 2, 2, 8, 9, 0, 6, 9, 8, 5, 7, 4, 8, 4, 7, 4, 2, 7, 9, 0, 8, 0, 6, 9, 7, 9, 9, 1, 6, 1, 3, 9, 9, 8, 9, 5, 5, 7, 8, 2, 0, 5, 1, 2, 8, 1, 4, 6, 6, 2, 6, 3, 8, 1, 7, 5, 2, 4, 8, 6, 2, 9, 7, 7, 8, 9, 9, 0, 3, 0, 8, 5, 3, 3, 0, 1, 2, 5, 6, 2, 8, 5, 4, 3, 0, 4, 8, 6, 9, 1, 8, 6, 4, 8, 1, 2
(list; graph; listen)
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OFFSET
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1,2
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EXAMPLE
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x=1.408494279228906985748474279080697991613998955782051281466263817524862977...
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) {PQ(n)=if(n%2==1, (n+1)/2, 2*PQ(n/2))} {CFM=contfracpnqn(vector(500, n, PQ(n))); x=CFM[1, 1]/CFM[2, 1]*1.0}
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CROSSREFS
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Cf. A109168 (continued fraction of x), A109170 (continued fraction of 2*x), A109171 (digits of 2*x).
Sequence in context: A020763 A137323 A021075 this_sequence A011291 A078889 A154847
Adjacent sequences: A109166 A109167 A109168 this_sequence A109170 A109171 A109172
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jun 21 2005
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