Re: [numbertheory] prime modulo 10 power two function of gaps--> corrected function

• To: mathgroup at smc.vnet.net
• Subject: [mg52025] Re: [numbertheory] prime modulo 10 power two function of gaps--> corrected function
• From: Roger Bagula <tftn at earthlink.net>
• Date: Sun, 7 Nov 2004 01:04:24 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Corrected function:
digits=200
f[n_]=16*Exp[(Log[2]/2)*(Mod[Prime[n],10]-Mod[Prime[n-1],10])]
a=Table[f[n],{n,3,digits-2}]
ListPlot[a,PlotJoined->True]

{32,32,2,32,64,32,2,128,1,128,2,32,64,4,128,1,128,2,32,128,2,128,8,2,32,64,32,

2,64,2,128,32,16,1,128,4,64,4,128,1,16,32,64,32,1,32,64,32,2,128,1,16,128,4,
128,1,128,2,32,16,64,2,32,64,2,128,16,32,2,128,8,4,128,2,128,8,2,256,16,1,
16,32,128,2,128,8,2,32,64,32,8,2,256,2,128,1,32,8,128,16,4,128,1,128,16,4,

128,1,128,4,64,32,1,16,32,64,4,128,1,32,64,4,8,16,256,16,8,4,128,2,8,128,2,

256,2,64,16,32,1,16,32,64,32,16,2,64,32,2,64,2,32,64,16,2,256,16,8,2,128,4,
64,2,128,4,8,128,32,2,128,1,16,32,128,16,1,16,32,128,8,2,32,64,4,128,8,4,
128,1,32,16,8,16,128,4,8,32}

Roger Bagula wrote:

>  Some time in the past a Louville number was made based on
>
>the modulo ten of the Primes past 5
>which have a digit set  of (1,3,7 ,9) and a magic square
>multiplication table.
>f[n]=10-Mod[Prime[n],10]
>I noticed that their gap had  a form like:
>2*Log[x]/Log[2]->x
>That fact  led with some experimentaion to the integer sequence in
>powers of two (skipping 4) as an exponential function.
>With both Sqrt[2] and Exp[] as parts of it, amazingly it is always an
>integer.
>That result makes it a "special" function like a Binet.
>
>
>(* prime modulo 10 power two function of gaps : set=(1,2,8,16)*)
>digits=200
>f[n_]=Exp[(Log[2]/2)*(Mod[Prime[n],10]-Mod[Prime[n-1],1])]/Sqrt[2]
>a=Table[f[n],{n,2,digits-2}]
>ListPlot[a,PlotJoined->True]
>
>{2,4,8,1,2,8,16,2,16,1,8,1,2,8,2,16,1,8,1,2,16,2,16,8,1,2,8,16,2,8,1,8,16,16,
>
>1,8,2,8,2,16,1,1,2,8,16,1,2,8,16,2,16,1,1,8,2,16,1,8,1,2,2,8,1,2,8,1,8,8,16,
>
>2,16,8,2,16,2,16,8,1,16,16,1,1,2,16,2,16,8,1,2,8,16,8,1,16,2,16,1,2,1,8,8,2,
>
>16,1,8,8,2,16,1,8,2,8,16,1,1,2,8,2,16,1,2,8,2,1,1,16,16,8,2,16,2,1,8,1,16,2,
>
>8,8,16,1,1,2,8,16,16,2,8,16,2,8,1,2,8,8,1,16,16,8,1,8,2,8,1,8,2,1,8,16,2,16,
>  1,1,2,16,16,1,1,2,16,8,1,2,8,2,16,8,2,16,1,2,2,1,1,8,2,1,2}
>Respectfully, Roger L. Bagula
>
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--
Respectfully, Roger L. Bagula