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

1,4

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A049283 A141162 A160035 * A353154 A325962 A210451

Adjacent sequences: A281645 A281646 A281647 * A281649 A281650 A281651

Keyword

nonn

Author

Seiichi Manyama, Jan 26 2017

Status

approved