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MathGroup Archive 2004

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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


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