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A281648 (Numerator of Bernoulli(2*n)) read mod n.

%I A281648 #35 Jan 28 2017 14:44:04
%S A281648 0,1,1,3,0,5,0,7,1,9,0,5,0,7,5,15,0,11,0,9,1,11,0,13,0,13,19,7,0,19,0,
%T A281648 31,11,17,0,11,0,19,13,13,0,37,0,33,35,23,0,37,0,39,34,39,0,11,5,35,
%U A281648 19,29,0,29,0,31,61,63,0,55,0,51,23,21,0,43,0,37,50,19
%N A281648 (Numerator of Bernoulli(2*n)) read mod n.
%C A281648 Conjecture: a(n) == n-1 (mod n) if only if n = 6, 10 or n = 2^k for k >= 0. This is true for n <= 1024. - _Seiichi Manyama_, Jan 27 2017
%H A281648 Seiichi Manyama, <a href="/A281648/b281648.txt">Table of n, a(n) for n = 1..1000</a>
%F A281648 a(n) = A000367(n) mod n.
%t A281648 f[n_] := Mod[Numerator[BernoulliB[2 n]], n]; Array[f, 77] (* _Robert G. Wilson v_, Jan 26 2017 *)
%o A281648 (Ruby)
%o A281648 def bernoulli(n)
%o A281648   ary = []
%o A281648   a = []
%o A281648   (0..n).each{|i|
%o A281648     a << 1r / (i + 1)
%o A281648     i.downto(1){|j| a[j - 1] = j * (a[j - 1] - a[j])}
%o A281648     ary << a[0]
%o A281648   }
%o A281648   ary
%o A281648 end
%o A281648 def A281648(n)
%o A281648   a = bernoulli(2 * n)
%o A281648   (1..n).map{|i| a[2 * i].numerator % i}
%o A281648 end
%o A281648 (PARI) a(n)=numerator(bernfrac(2*n))%n \\ _Charles R Greathouse IV_, Jan 27 2017
%Y A281648 Cf. A000367, A060976, A069040, A070192, A070193, A281662.
%K A281648 nonn
%O A281648 1,4
%A A281648 _Seiichi Manyama_, Jan 26 2017