A090495 Numbers n such that numerator(Bernoulli(2*n)/(2*n)) is different from numerator(Bernoulli(2*n)/(2*n*(2*n-1))). 12 574, 1185, 1240, 1269, 1376, 1906, 1910, 2572, 2689, 2980, 3238, 3384, 3801, 3904, 4121, Michael Somos <http://oeis.org/wiki/User:Michael_Somos> (Feb 01 2004) discovered the remarkable fact that A001067 <http://oeis.org/A001067> is different from A046968 <http://oeis.org/A046968>, even though they agree for the first 573 terms. Hey, Bernoulli(n+1)/n/(n+1) agrees with Bernoulli(n+1)/(n+1) for 1147 terms! Do[If[Numerator[BernoulliB[n + 1]/n/(n + 1)] != Numerator[BernoulliB[n + 1]/(n + 1)], Print[n.GCD[n, Numerator[BernoulliB[n + 1]/(n + 1)]]]], {n, 3511}] // tim 1147.37 2369.103 2479.37 2537.59 2751.131 8.898235 secs (Don't laugh. You should usually think in terms of Bernoulli *polynomials* .) As http://mathworld.wolfram.com/StirlingsSeries.html points out, Bernoulli(2*n)/(2*n*(2*n-1))) are the coefficients of the (divergent) Stirling series I mentioned yesterday. --rwg Mathematica now has anagrams: "deeeiimnorsstt" -> {"endometritises", "densitometries"}, ... "adegiiinnorstt" -> {"disorientating", "disintegration"}, ... "aeegiinorrsttv" -> {"tergiversation", "interrogatives"}, ... "eiinoopprssstu" -> {"superpositions", "propitiousness"}, ... Except that endometritises should be endometritides, which it doesn't even know: In[903]:= DictionaryWordQ@"endometritides" Out[903]= False