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A123251
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Continued fraction for sqrt(2)*tan(1/sqrt(2)).
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0
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1, 4, 1, 3, 1, 12, 1, 7, 1, 20, 1, 11, 1, 28, 1, 15, 1, 36, 1, 19, 1, 44, 1, 23, 1, 52, 1, 27, 1, 60, 1, 31, 1, 68, 1, 35, 1, 76, 1, 39, 1, 84, 1, 43, 1, 92, 1, 47, 1, 100, 1, 51, 1, 108, 1, 55, 1, 116, 1, 59, 1, 124, 1, 63, 1, 132, 1, 67, 1, 140, 1, 71, 1, 148, 1, 75, 1, 156, 1, 79, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This continued fraction allows us to see that tan(1/sqrt(2)), sin(1/sqrt(2)), cos(1/sqrt(2)) are irrationnal. More generally, for any fixed positive integer m, the continued fraction for sqrt(m)*tan(1/sqrt(m)) is given by : a(12n-11)=a(12n-9)=a(12n-7)=a(12n-5)=a(12n-3)=a(12n-1)=1; a(12n-10)=12*m*n-9*m-2 ; a(12n-8)=12n-9 ; a(12n-6)=12*m*n-5*m-2 ; a(12n-4)=12n-5 ; a(12n-2)=12*m*n-m-2 ; a(12n)=12n-1
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FORMULA
| For n>=1 we have a(12n-11)=a(12n-9)=a(12n-7)=a(12n-5)=a(12n-3)=a(12n-1)=1; a(12n-10)=24n-20 ; a(12n-8)=12n-9 ; a(12n-6)=24n-12 ; a(12n-4)=12n-5 ; a(12n-2)=24n-4 ; a(12n)=12n-1
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CROSSREFS
| Cf. A123168.
Sequence in context: A010127 A055032 A039930 * A021246 A197840 A019633
Adjacent sequences: A123248 A123249 A123250 * A123252 A123253 A123254
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (abmt(AT)orange.fr), Oct 08 2006
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