Bernoulli numbers

[Edwin Clark]

> 
> Dear SeqFans,   Michael Somos made an interesting discovery.
> A001067 and A046968 are not the same!
> In fact: (speaking baby Mathematica talk, which is
> all that i know): 
> 
> a[n_] := Numerator[BernoulliB[2n]/(2n)]          (* A001067 *)
> b[n_] := Numerator[BernoulliB[2n]/(2n(2n-1))]    (* A046968 *)
> 
> For[n=1, n <= 580, n++, 
> If[ a[n] != b[n], Print[n, " ", a[n]/b[n]] ]
> ]
> 
> produces one line of output
> 
>                   574 37
> 
> In other words, the sequence of values of n such that
> A001067(n) differs from A046968(n) starts
> 574, ...
> and the associated ratios begin
> 37, ...
> 
> Could someone with more computing power than I have extend
> these two sequences?  PARI gives the same result.  Maple dies.
> 

Hmm... Maple didn't die on me (this time!) Here's what I got
taking n up to 2000:

> a:=n->numer(bernoulli(2*n)/(2*n)):
> b:=n->numer(bernoulli(2*n)/(2*n*(2*n-1))):
> for n from 1 to 2000 do
> if a(n)<>b(n) then print(n,a(n)/b(n));  fi;
> od:

                                574, 37
                               1185, 103
                               1240, 37
                               1269, 59
                               1376, 131
                               1906, 37
                               1910, 67


--Edwin