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Search: id:A119814
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| A119814 |
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Numerators of the convergents to the continued fraction for the constant A119812 defined by binary sums involving Beatty sequences: c = Sum_{n>=1} A049472(n)/2^n = Sum_{n>=1} 1/2^A001951(n). |
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+0
3
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| 0, 1, 6, 109, 112494, 1887350536045, 543991754934632523092182415214, 758213844806172103575972149363453352380811718063209070444420739586832237
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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The number of digits in these numerators are (beginning at n=2): [1,1,3,6,13,30,72,174,420,1013,2444,5901,14245,34391,83027,...].
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EXAMPLE
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c = 0.858267656461002055792260308433375148664905190083506778667684867..
Convergents begin:
[0/1, 1/1, 6/7, 109/127, 112494/131071, 1887350536045/2199023255551,..]
where the denominators of the convergents equal [2^A001333(n-1)-1]:
[1,1,7,127,131071,2199023255551,633825300114114700748351602687,...]
and A001333 is numerators of continued fraction convergents to sqrt(2).
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PROGRAM
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(PARI) {a(n)=local(M=contfracpnqn(vector(n, k, if(k==1, 0, if(k==2, 1, 4^round(((1+sqrt(2))^(k-2)+(1-sqrt(2))^(k-2))/(2*sqrt(2))) +if(k==3, 2, 2^round(((1+sqrt(2))^(k-3)-(1-sqrt(2))^(k-3))/2))))))); return(M[1, 1])}
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CROSSREFS
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Cf. A119812 (constant), A119813 (continued fraction), A001333; A119809 (dual constant).
Sequence in context: A012503 A132856 A041149 this_sequence A050884 A156554 A112499
Adjacent sequences: A119811 A119812 A119813 this_sequence A119815 A119816 A119817
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KEYWORD
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frac,nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), May 26 2006
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