Re: : huge number, ciphers after decimal point?

*To*: mathgroup at smc.vnet.net*Subject*: [mg36537] Re: : huge number, ciphers after decimal point?*From*: larry <goldbach at charter.net>*Date*: Wed, 11 Sep 2002 03:28:02 -0400 (EDT)*References*: <200204060548.AAA24777@smc.vnet.net> <a8rgtl$b57$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Fred Simons wrote: > Stefan, > > To find n digits before the decimal point of a number, we can proceed in the > following way. We compute the number in sufficiently many digits, then take > the Floor of the result (i.e. we round it downwards to an integer) and > finally take the result modulo 10^n. > > Mod[Floor[ N[(Sqrt[2] + Sqrt[3])^2002 , 1000]], 10^2] > > results in 9, so the last two digits before the decimal point are 09. > > With a slight modification we can find the first n digits after the decimal > point. Simply find the last n digits before the decimal point of 10^n times > the number. > > Mod[Floor[ N[10^2 (Sqrt[2] + Sqrt[3])^2002 , 1000]], 10^2] > > results in 99, so these are the digits you are interested in. > > But there is something curious about this number. > > Mod[Floor[N[10^1000 (Sqrt[2] + Sqrt[3])^2002 , 2000]], 10^1000] > > results in 996 digits 9 followed by 7405. > > You can also play with the following command, resulting in the digits around > the decimal point: > > Mod[ N[(Sqrt[2] + Sqrt[3])^2002, 2300], 10^6] > > The decimal expansion of (Sqrt[2]+Sqrt[3])^2002 contains a sequence of > 997 consecutive digits 9. Do you have any idea why? Not unusual. Try other even exponents and there should be large blocks of 9s . Smaller number for small exponents. Some kind of propagation of 9s as the exponent grows. Try other odd values for 3 and the same thing happens for some values. Also for other values for 2. Larry > > Fred Simons > Eindhoven University of Technology > > > > >