Bernoulli numbers and arithmetic progressions

[Hans Havermann]

On Feb 4, 2004, at 6:55 AM, Roland Bacher wrote:

> all values yielding 37 are of the form: 574+666*k, k=0,1,2,3,4,...
> and form thus an arithmetic progression with step 
> 666=18*37=((37-1)/2)*37;

Very vice.

Here are the data points (<10000):

{574, 37}, {1185, 103}, {1240, 37}, {1269, 59}, {1376, 131}, {1906, 
37}, {1910, 67}, {2572, 37}, {2689, 283}, {2980, 59}, {3238, 37}, 
{3384, 101}, {3801, 691}, {3904, 37}, {4121, 67}, {4570, 37}, {4691, 
59}, {4789, 157}, {5236, 37}, {5862, 617}, {5902, 37}, {6227, 593}, 
{6332, 67}, {6402, 59}, {6438, 103}, {6568, 37}, {7234, 37}, {7900, 
37}, {8113, 59}, {8434, 101}, {8543, 67}, {8557, 157}, {8566, 37}, 
{9232, 37}, {9611, 149}, {9670, 233}, {9824, 59}, {9891, 131}, {9898, 
37}

So, empirically, not one miss for 37.