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

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, 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, 19, 29, 0, 29, 0, 31, 61, 63, 0, 55, 0, 51, 23, 21, 0, 43, 0, 37, 50, 19

Offset: 1

Author

Seiichi Manyama, Jan 26 2017

Keywords

• nonn

Comments

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

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000367, A060976, A069040, A070192, A070193, A281662.

Programs

Mathematica

f[n_] := Mod[Numerator[BernoulliB[2 n]], n]; Array[f, 77] (* Robert G. Wilson v, Jan 26 2017 *)

PARI

a(n)=numerator(bernfrac(2*n))%n \\ Charles R Greathouse IV, Jan 27 2017

Ruby

def bernoulli(n)
  ary = []
  a = []
  (0..n).each{|i|
    a << 1r / (i + 1)
    i.downto(1){|j| a[j - 1] = j * (a[j - 1] - a[j])}
    ary << a[0]
  }
  ary
end
def A281648(n)
  a = bernoulli(2 * n)
  (1..n).map{|i| a[2 * i].numerator % i}
end

Formula

a(n) = A000367(n) mod n.