/* A 20-term relation communicated 27-October-2010 by Amrik Singh Nimbran: [1]= +517318131[3739944528] +426029142[3816349818] +829834652[4038832337] +768770095[5760773543] -205626937[6608082112] +87613144[8529242966] +1750813914[18710140581] +772632722[20875536277] +1650135768[24858161060] +498268105[29546599818] -564526926[44356375201] +37263672[94111829193] +1030074814[102416588812] -1027928612[113201494333] +1587889662[246207915091] +1185772517[265542904947] +1160619249[378137211957] +1809488853[1628612367538] -672270548[3737240479718] -223375218[11830545643782] Primes: {5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 149, 173, 193, 313, 409, 509, 977, 1409} Note the primes 977 and 1409 which where out of range with my 2006 search (using primes <=761) Verify the relation numerically with pari/gp via gp < arctan-20term-nimbran.gp (see end of file) */ \\default(echo,1); default(realprecision, 10000); \\ decimal digits default(format,"g.55"); A(x)=atan(1/x); { -1 * A(1) +517318131*A(3739944528) \\ 1 +426029142*A(3816349818) \\ 2 +829834652*A(4038832337) \\ 3 +768770095*A(5760773543) \\ 4 -205626937*A(6608082112) \\ 5 +87613144*A(8529242966) \\ 6 +1750813914*A(18710140581) \\ 7 +772632722*A(20875536277) \\ 8 +1650135768*A(24858161060) \\ 9 +498268105*A(29546599818) \\ 10 -564526926*A(44356375201) \\ 11 +37263672*A(94111829193) \\ 12 +1030074814*A(102416588812) \\ 13 -1027928612*A(113201494333) \\ 14 +1587889662*A(246207915091) \\ 15 +1185772517*A(265542904947) \\ 16 +1160619249*A(378137211957) \\ 17 +1809488853*A(1628612367538) \\ 18 -672270548*A(3737240479718) \\ 19 -223375218*A(11830545643782) \\ 20 } quit; /* Test run: % gp < arctan-20term-nimbran.gp -1.2602298323052254416 E-10018 */