Bernoulli numbers and arithmetic progressions

[cino hilliard]

>From: "Eric W. Weisstein" <eww at wolfram.com>
>To: cino hilliard <hillcino368 at hotmail.com>
>Subject: Re: Bernoulli numbers and arithmetic progressions
>Date: Sat, 14 Feb 2004 23:24:23 -0600 (CST)
>
>On Wed, 4 Feb 2004, cino hilliard wrote:
>
> >
> > >From: "Eric W. Weisstein" <eww at wolfram.com>
>Actually, I'm done with this problem for now, but please feel free to
>pursue the search further.
>
>Thanks,
>-Eric

Thanks Eric ,
I will compute some more terms. So far I have

Subject: COMMENT FROM Cino Hilliard RE A090495
574,1185,1240,1269,1376,1906,1910,2572,2689,2980,3238,3384,3801,3904,4121,4570,
4691,4789,5236,5862,5902,6227,6332,6402,6438,6568,7234,7900,8113,8434,8543,8557,
8566,9232,9611,9670,9824,9891,9898,10564,10587,10754,11230,11247,11535,11691,
11896,12562,12965,13019,13228,13246,13355,13484,13894,14560,14714,14957,15176,
15226,15346,15892,16558,16668,16944,17035,17224,17387,17890,18379,18406,18534,
18556,18761,19222,19598,19888,20090

The Pari program below is a simpler version that only makes one bernfrac 
call
per iteration. This should reduce the calc time by about 1/2. The same will 
hold true for
b = numerator(a/(n2+1)). Actually, we can generate the irregular primes by 
testing
b = a/(n2+r) for r = 2,3,5,7...prime.

I am tracking these in the Excel spread sheet at

          http://groups.yahoo.com/group/B2LCC/files/Bernoulli/



bern2(c,m1,m2) =
       {
       for(n=m1,m2,
          n2=n+n;
          a = numerator(bernfrac(n2)/(n2));          \ \ A001067
          b = numerator(a/(n2-1));
          if(a <>b; b,print("A("c") = "n","a/b);c++)
          )
       }

Cino

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