

A171245


Reciprocals of the deviation of continued fraction convergents from Pi.


0



7, 790, 12016, 3748629, 1730431227, 3015428685, 8172837003, 34313104062, 114738541304, 620832653094, 2474837590227, 45157370341559, 1726856191927439, 6094457427533473, 12791098836150787, 51642743340781227, 325724575136738920, 1813676066719263909
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Clearly the terms alternate in sign, but the initial choice of sign was arbitrary.


LINKS

Table of n, a(n) for n=1..18.


EXAMPLE

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.


PROG

(PARI) for(x=1, 10, t=contfracpnqn(contfrac(Pi, x)); print(truncate(1/(Pit[1, 1]/t[2, 1]))))


CROSSREFS

Cf. A001203.
Sequence in context: A162089 A020470 A182282 * A014013 A001467 A342836
Adjacent sequences: A171242 A171243 A171244 * A171246 A171247 A171248


KEYWORD

sign


AUTHOR

Phil Carmody, Dec 06 2009


EXTENSIONS

More terms from Jinyuan Wang, Aug 23 2021


STATUS

approved



