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Search: id:A070154
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| A070154 |
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Number of terms in the simple continued fraction expansion of Sum(k=0,n,(-1)^k/(2k+1)), the Leibniz-Gregory series for Pi. |
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+0
1
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| 3, 4, 9, 5, 9, 14, 10, 10, 19, 16, 21, 22, 22, 24, 20, 19, 24, 28, 28, 29, 30, 39, 31, 44, 40, 44, 33, 41, 47, 44, 48, 54, 48, 60, 49, 63, 51, 65, 72, 64, 70, 78, 64, 79, 77, 74, 87, 75, 86, 82, 94, 88, 106, 106, 94, 104, 108, 87, 107, 86, 106, 98, 110, 115, 110, 105, 115
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Pi/4=Sum(k=>0,(-1)^k/(2k+1))
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FORMULA
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lim n -> infinity a(n)/n=C=1, 6...
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EXAMPLE
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The simple continued fraction for Sum(k=0,10,(-1)^k/(2k+1)) is [0, 1, 4, 4, 1, 3, 54, 1, 2, 1, 1, 4, 11, 1, 2, 2] which contains 16 elements, hence a(10)=16.
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PROGRAM
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(PARI) for(n=1, 100, print1( length(contfrac(sum(i=0, n, (-1)^i/(2*i+1)))), ", "))
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CROSSREFS
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Cf. A055573, A069880, A069887.
Sequence in context: A083437 A011292 A021745 this_sequence A023183 A102320 A021290
Adjacent sequences: A070151 A070152 A070153 this_sequence A070155 A070156 A070157
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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), May 06 2002
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