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A171245
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Reciprocals of the deviation of continued fraction convergents from Pi.
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0
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7, -790, 12016, -3748629, 1730431227, -3015428685, 8172837003, -34313104062, 114738541304, -620832653094, 2474837590227, -45157370341559, 1726856191927439, -6094457427533473, 12791098836150787, -51642743340781227, 325724575136738920, -1813676066719263909
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OFFSET
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1,1
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COMMENTS
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Clearly the terms alternate in sign, but the initial choice of sign was arbitrary.
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LINKS
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EXAMPLE
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The first convergent to Pi, 3, is just over 1/7 too low, so 7 is the first term.
The second convergent, 22/7, is 0.001264+ too high, which is just over 1/790, so -790 is the second term.
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PROG
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(PARI) for(x=1, 10, t=contfracpnqn(contfrac(Pi, x)); print(truncate(1/(Pi-t[1, 1]/t[2, 1]))))
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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