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Search: id:A071915
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| A071915 |
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Number of 1's in continued fraction expansion of (3/2)^n. |
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+0
1
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| 0, 0, 1, 0, 2, 3, 3, 6, 3, 5, 1, 2, 8, 2, 3, 5, 2, 3, 3, 6, 10, 8, 6, 4, 2, 3, 6, 5, 2, 9, 12, 7, 17, 10, 7, 9, 8, 10, 13, 13, 10, 12, 14, 9, 11, 10, 11, 6, 9, 5, 3, 13, 13, 19, 18, 13, 8, 12, 15, 14, 18, 7, 19, 19, 17, 15, 13, 14, 16, 13, 20, 16, 10, 20, 25, 17, 19, 14, 19, 14, 18, 22
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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It seems that lim n ->infinity a(n)/n = 0,2... << (ln(4)-ln(3))/ln(2) = 0,415... the expected density of 1's (cf. measure theory of continued fraction)
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EXAMPLE
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The continued fraction of (3/2)^24 is [16834, 8, 1, 10, 2, 25, 1, 3, 1, 1, 57, 6] which contains 4 "1's", hence a(24)=4
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PROGRAM
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(PARI) for(n=1, 200, s=contfrac(frac((3/2)^n)); print1(sum(i=1, length(s), if(1-component(s, i), 0, 1)), ", "))
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CROSSREFS
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Cf. A071337, A071316, A071315, A071529.
Sequence in context: A046826 A054892 A104570 this_sequence A021432 A141729 A049990
Adjacent sequences: A071912 A071913 A071914 this_sequence A071916 A071917 A071918
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 13 2002
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