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Search: id:A102367
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| A102367 |
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(Numerator of n-th convergent to Pi having an even numerator)/2. |
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+0
1
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| 11, 52174, 573204, 122925461, 534483448, 3083975227, 2685575996367, 214112296674652, 131226315167691099699, 396325638628212603442, 5947531272548328355975, 118554299812338354516058
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Abs[Cos[a(n)]] approaches 0; Abs[Sin[a(n)]] approaches 1.
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LINKS
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Eric Weisstein's World of Mathematics, "Convergent."
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EXAMPLE
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a(1)=11 because the first convergent of Pi with an even numerator is 22/7
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MATHEMATICA
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Select[Table[1/2*Numerator[FromContinuedFraction[ContinuedFraction[Pi, k][[Range[1, k]]]]], {k, 1, 60}], IntegerQ]
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CROSSREFS
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Cf. A002485.
Adjacent sequences: A102364 A102365 A102366 this_sequence A102368 A102369 A102370
Sequence in context: A076783 A145526 A068647 this_sequence A055322 A165934 A110780
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KEYWORD
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base,nonn
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AUTHOR
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Joseph Biberstine (jrbibers(AT)indiana.edu), Feb 22 2005
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