New polynomial set that yields a sequence set of real irrational numbers

*To*: mathgroup at smc.vnet.net*Subject*: [mg47652] New polynomial set that yields a sequence set of real irrational numbers*From*: "Roger L. Bagula" <rlbtftn at netscape.net>*Date*: Tue, 20 Apr 2004 03:19:10 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Mathematica code for the sequence: f[p_]=Sum[1/p^n,{n,1,m}] Table[NSolve[f[p]+1/p-p==0,p],{m,1,15}] m=Infinity aa=Sum[1/p^n,{n,1,m}] NSolve[aa+1/p-p==0,p] let d(0)=1.41421 let d(1)=1.6180339 let d(2)=1.71064 let d(3)=1.75488 let d(4)=1.77704 let d(5)=1.78854 let d(6)=1.79465 let d(7)=1.79794 let d(8)=1.79974 let d(9)=1.80072 let d(10)=1.80127 let d(11)=1.80157 let d(12)=1.80173 let d(13)=1.80182 let d(14)=1.80187 let d(Infinity)=1.80194 This sequence was discovered as the result of an experimental IFS fractal program. Respectfully, Roger L. Bagula