/*
A 25-term relation communicated 23-July-2010 by Amrik Singh Nimbran:

 3[1] =
 +56019074327[218123852367]
 -74085743[221943811240]
 +68050753395[250645741818]
 +105797200464[261002206018]
 +201629004998[261217252912]
 +45630089711[269007136889]
 +236222905926[548275361132]
 -5352379798[656902304557]
 -103707336253[662573197307]
 +169672134301[1372432573478]
 +133389216526[2105653391693]
 -26696176904[3761284561432]
 -6722906188[5142102426318]
 +145182881844[5745192731179]
 -223092042480[8589803519307]
 +196241475455[10892900268195]
 +113882868171[17780261434697]
 +336178399031[25331597869589]
 -13647444377[38759264489343]
 +46026949849[165171481279982]
 -6884159866[169838669284032]
 -190645533827[342036110675693]
 +211179728284[772654028018543]
 +175868593760[1948025182233307]
 -165372390023[1976865441422893]

 Primes: {5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101,
     109, 137, 229, 257, 281, 337, 353, 433, 461, 593, 601, 941}
 Note the prime 941 which was out of range with
 my 2006 search (using primes <=761)

Verify the relation numerically with pari/gp via
gp < arctan-25term-nimbran.gp
(see end of file)
*/

\\default(echo,1);
default(realprecision, 10000);  \\ decimal digits
default(format,"g.55");

A(x)=atan(1/x);

{
 -3 * A(1)
 +56019074327 * A(218123852367) \\ 1
 -74085743 * A(221943811240) \\ 2
 +68050753395 * A(250645741818) \\ 3
 +105797200464 * A(261002206018) \\ 4
 +201629004998 * A(261217252912) \\ 5
 +45630089711 * A(269007136889) \\ 6
 +236222905926 * A(548275361132) \\ 7
 -5352379798 * A(656902304557) \\ 8
 -103707336253 * A(662573197307) \\ 9
 +169672134301 * A(1372432573478) \\ 10
 +133389216526 * A(2105653391693) \\ 11
 -26696176904 * A(3761284561432) \\ 12
 -6722906188 * A(5142102426318) \\ 13
 +145182881844 * A(5745192731179) \\ 14
 -223092042480 * A(8589803519307) \\ 15
 +196241475455 * A(10892900268195) \\ 16
 +113882868171 * A(17780261434697) \\ 17
 +336178399031 * A(25331597869589) \\ 18
 -13647444377 * A(38759264489343) \\ 19
 +46026949849 * A(165171481279982) \\ 20
 -6884159866 * A(169838669284032) \\ 21
 -190645533827 * A(342036110675693) \\ 22
 +211179728284 * A(772654028018543) \\ 23
 +175868593760 * A(1948025182233307) \\ 24
 -165372390023 * A(1976865441422893) \\ 25
}


quit;
/*
Test run:
% gp < arctan-25term-nimbran.gp
-2.196184169870468284 E-10018

*/