Fibonacci based sum that is b-normal on binary numbers

*To*: mathgroup at smc.vnet.net*Subject*: [mg52117] Fibonacci based sum that is b-normal on binary numbers*From*: Roger Bagula <tftn at earthlink.net>*Date*: Thu, 11 Nov 2004 04:52:29 -0500 (EST)*Reply-to*: tftn at earthlink.net*Sender*: owner-wri-mathgroup at wolfram.com

This sum and it's b-normal sequence is due to work of a friend who doesn't like me to use his name here or elsewhere .He came up with two very nice sums using Fibonacci numbers. I used the Binet function in them and got very good agreement. So I tried them in a b-normal. I had to modify the result some to get this result. I get a new sum that appears irrational and an iteration that is b-normal . I think that using the Binet function in this makes it a new sequence sum. I thought that this was a very remarkable result. Clear[x,a,digits,f,fib] (* convergent sum based on Fibonacci sequence to make a binary b-normal iteration *) digits=200 fib[n_Integer?Positive] :=fib[n] = fib[n-1]+fib[n-2] fib[0]=0;fib[1] = fib[2] = 1; sfib=Sum[fib[n]/((n+1)*2^(n+1)),{n,0,digits}] N[sfib,digits] x[n_]:=x[n]=Mod[2*x[n-1]+fib[n-1]/(2*n),1] x[0]=0 a=Table[N[x[n],digits],{n,0,digits}] ListPlot[a,PlotJoined->True,PlotRange->All] b=Sort[Table[N[x[n],digits],{n,0,digits}]]; ListPlot[b,PlotJoined->True,PlotRange->All] Respectfully, Roger L. Bagula tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 : alternative email: rlbtftn at netscape.net URL : http://home.earthlink.net/~tftn