/*
A 24-term relation communicated 23-July-2010 by Amrik Singh Nimbran:

22[1] =
+407688507599[121409547033]
+131623078258[138873731225]
+597669985516[148431551771]
-252429143056[168722145007]
+862365372722[202954204459]
+87197344668[221943811240]
+834204536395[261002206018]
+418763705566[269007136889]
+756410649259[548275361132]
-116186529925[656902304557]
-257884015194[662573197307]
+338026625427[1372432573478]
-202652185491[2105653391693]
+163956958098[3761284561432]
-5430991987[5142102426318]
+88783805991[5745192731179]
+415733461899[10892900268195]
-239380754897[17780261434697]
+27932108979[38759264489343]
-114027862098[165171481279982]
+378900051128[169838669284032]
-414020468150[772654028018543]
-199714577789[1948025182233307]
-280710519362[1976865441422893]

Primes: {5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101,
 109, 137, 229, 257, 281, 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-24term-nimbran.gp
(see end of file)
*/

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

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

{
-22 * A(1)
+407688507599 * A(121409547033) \\ 1
+131623078258 * A(138873731225) \\ 2
+597669985516 * A(148431551771) \\ 3
-252429143056 * A(168722145007) \\ 4
+862365372722 * A(202954204459) \\ 5
+87197344668 * A(221943811240) \\ 6
+834204536395 * A(261002206018) \\ 7
+418763705566 * A(269007136889) \\ 8
+756410649259 * A(548275361132) \\ 9
-116186529925 * A(656902304557) \\ 10
-257884015194 * A(662573197307) \\ 11
+338026625427 * A(1372432573478) \\ 12
-202652185491 * A(2105653391693) \\ 13
+163956958098 * A(3761284561432) \\ 14
-5430991987 * A(5142102426318) \\ 15
+88783805991 * A(5745192731179) \\ 16
+415733461899 * A(10892900268195) \\ 17
-239380754897 * A(17780261434697) \\ 18
+27932108979 * A(38759264489343) \\ 19
-114027862098 * A(165171481279982) \\ 20
+378900051128 * A(169838669284032) \\ 21
-414020468150 * A(772654028018543) \\ 22
-199714577789 * A(1948025182233307) \\ 23
-280710519362 * A(1976865441422893) \\ 24
}


quit;
/*
Test run:
% gp < arctan-24term-nimbran.gp
-1.9778779060308370354 E-10017
? quit;

*/