A133450: correction, more terms, Mmca

[zak seidov]

Of interest is
A075190  Numbers n such that n^2 is an interprime =
average of two successive primes.
  
--- Maximilian Hasler <maximilian.hasler at gmail.com>
wrote:

> Since n^2-1 is never prime but n^2+1 has much better
> chance of being
> prime, the average is much more often less than n^2
> and the sum grows
> steadily:
> 
> (09:10) gp >
> A056929(i)=i^2-(nextprime(i^2)+precprime(i^2))/2
> time = 0 ms.
> (09:10) gp > sum(i=1,10^3,A056929(i))
> time = 0 ms.
> %1 = 168
> (09:10) gp > sum(i=1,10^4,A056929(i))
> time = 188 ms.
> %2 = 1664
> (09:10) gp > sum(i=1,10^5,A056929(i))
> time = 4,703 ms.
> %3 = 19906
> 
> On Dec 26, 2007 6:24 PM, Alexander Povolotsky
> <apovolot at gmail.com> wrote:
> > Before submitting sequences I typically run it via
> superkeeper to
> > avoid duplication.
> > Obviously the superkeeper is not capable to
> pick-up cases when one
> > sequence is "1/2" (every second term) subset of
> existing one.
> >
> > Further, I do have a question related to both
> A056929 and A133450.
> >
> > Based on the 100 terms in A133450, calculated by
> Zak Seidov
> > the (so far) running sum of terms is:
> >
> >
>
0+1+2+0+1+0+1+2+0+1+1+2+1+4+3-2-2+2+1+1-4-5-5+1+10+1+3+7-2+0+4+0+3-5+4+0+2+12+0-9
> >
>
-2+6-6-3+3+0+2+1-3+10-9+1+10-3+1+0+4+2-2+5+1+1+8-12+5-1+8-2+0+0-3-1+1+2+8-4+12
> > +3+4+5+1-2-10+0+10+0-6+2+7+9-10+2-1-2-2+0-2+4+0+1=
> 89 (per 100).
> >
> > Based on the 87 terms in A056929 the (so far)
> running sum is:
> >
> > 0 + 0 + 1 - 1 + 2 - 1 + 0 + 0 + 1 + 1 + 0 - 1 + 1
> + 0 + 2 + 1 + 0 - 2
> > + 1 + 0 + 1 - 3 + 2 + 0 + 1 - 1 + 4 - 5 + 3 + 1 -
> 2 + 0 - 2 - 1 + 2 -
> > 1 + 1 + 4 + 1 + 0 - 4 - 5 - 5 + 3 - 5 - 1 + 1 - 4
> + 10 + 0 + 1 - 2 + 3
> > - 5 + 7 + 9 - 2 + 1 + 0 - 2 + 4 - 9 + 0 + 1 + 3 +
> 1 - 5 - 10 + 4 - 4 +
> > 0 + 1 + 2 - 6 + 12 - 4 + 0 + 3 - 9 + 3 - 2 - 2 + 6
> + 1 - 6 + 2 - 3 =
> > -7 (per 87)
> >
> > So the question is:
> >
> > Are squares of integers indeed on average located
> "more or less" in the
> > middle between bounding prime numbers ?
> > Are there any reference (currently none listed) to
> this question subject ?
> >
> > Alex
> >
>
===========================================================
> >
> > On Dec 26, 2007 4:26 PM, Maximilian Hasler
> <maximilian.hasler at gmail.com> wrote:
> > > this seq. appears to be just every other term of
> > >
> http://www.research.att.com/~njas/sequences/A056929
> > > Difference between n^2 and average of smallest
> prime greater than n^2
> > > and largest prime less than n^2.
> > > As such it becomes a bit less interesting in
> itself (IMHO)...
> > >
> > > %I A133450
> > > %S A133450 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 1, 2,
> 1, 4, 3, -2, -2
> > > %F A133450 a(n)=A056929(2n)
> > > %Y A133450 Cf. A056929
> > > %o A133450 (PARI)
>
A133450(n)=4*n^2-(precprime(4*n^2)+nextprime(4*n^2))/2
> > > %A A133450 Maximilian F. Hasler
> (Maximilian.Hasler(AT)gmail.com), Dec 26 2007
> > >
> > > In order not to mix up Neil's scripts, I resist
> against puting the
> > > obvious PARI code for A056929 in this very same
> e-mail (just remove
> > > the "4*"s) - anyway, that other seq. already has
> the corresponding
> > > Maple code.
> > >
> > > On Dec 23, 2007 4:32 PM, zak seidov
> <zakseidov at yahoo.com> wrote:
> > > > Neil, Alexander,
> > > >
> > > > 1.
> > > > %e A133450 a(5)=5 because 100 - (89 + 101)/2 =
> 5
> > > > should be
> > > > %e A133450 a(5)=1 because 100 - (97 + 101)/2 =
> 1
> > > >
> > > > 2.
> > > > More terms:
> > > >
> > > > %S A133450
> > > >
>
0,1,2,0,1,0,1,2,0,1,1,2,1,4,3,-2,-2,2,1,1,-4,-5,-5,1,10,1,3,7,-2,0,4,0,3,-5,4,0,2,12,0,-9,-2,6,-6,-3,3,0,2,1,-3,10,-9,1,10,-3,1,0,4,2,-2,5,1,1,8,-12,5,-1,8,-2,0,0,-3,-1,1,2,8,-4,12,3,4,5,1,-2,-10,0,10,0,-6,2,7,9,-10,2,-1,-2,-2,0,-2,4,0,1
> > > >
> > > > 3.
> > > > Mmca code:
> > > >
>
Table[n^2-(Prime[PrimePi[n^2]]+Prime[PrimePi[n^2]+1])/2,{n,2,200,2}]
> > > > - Zak Seidov (zakseidov at yahoo.com)
> > > >
> > >
> >
> 
> 
> 
> -- 
> Maximilian F. Hasler
> (Maximilian.Hasler(AT)gmail.com)
> 



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