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Search: id:A071940
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| A071940 |
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Number of 1's among the n first elements of the simple continued fraction for Pi. |
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+0
1
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| 0, 0, 0, 1, 1, 2, 3, 4, 4, 5, 5, 6, 6, 6, 7, 8, 8, 8, 8, 8, 9, 9, 9, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 15, 15, 15, 16, 16, 17, 17, 17, 17, 18, 18, 19, 20, 20, 21, 22, 23, 23, 24, 25, 25, 26, 27, 27, 28, 28, 29, 30, 30, 30, 30, 30, 31, 31, 31, 31
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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a(100)/100 = 0,41 Does lim n ->infinity a(n)/n = (Log(4)-Log(3)) / Log(2) =0,415... the expected density of "1's" ? (cf. measure theory of continued fraction)
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EXAMPLE
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Continued fraction for Pi begins : 3, 7, 15, 1, 292, 1, 1,.... there are 3 "1's" among the 7 first terms, hence a(7)=3.
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PROGRAM
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(PARI) for(n=1, 100, print1(sum(i=1, n, if(component(contfrac(Pi), i)-1, 0, 1)), ", "))
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CROSSREFS
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Cf. A001203.
Sequence in context: A131234 A056791 A027434 this_sequence A085883 A094192 A093874
Adjacent sequences: A071937 A071938 A071939 this_sequence A071941 A071942 A071943
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KEYWORD
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easy,nonn,cofr
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 15 2002
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