A162173 - OEIS

%I #25 Oct 07 2024 01:17:24

%S 0,5,31,41,31,61,3421,1,4127,43069,174941,854375,236366821,8553097,

%T 23749461899,8615841261683,7709321041727,2577687858361,

%U 26315271553055396563,2929993913841553,261082718496449135581

%N Absolute difference of numerator and denominator of Bernoulli(2*n), n >= 0.

%H Muniru A Asiru, <a href="/A162173/b162173.txt">Table of n, a(n) for n = 0..310</a>

%F a(n) = abs(A000367(n) - A002445(n)).

%e a(0) = abs(1 - 1) = 0.

%e a(1) = abs(1 - 6) = 5.

%e a(2) = abs(-1 - 30) = 31.

%p A000367 := proc(n) numer(bernoulli(2*n)) ; end: A002445 := proc(n) denom(bernoulli(2*n)) ; end: A162173 := proc(n) abs( A000367(n)-A002445(n)) ; end: seq(A162173(n),n=0..40) ; # _R. J. Mathar_, Sep 13 2009

%t a[n_] := Abs[Numerator[BernoulliB[2n]] - Denominator[BernoulliB[2n]]]; Array[a, 20, 0] (* _Amiram Eldar_, Nov 25 2018 *)

%t Abs[Denominator[#]-Numerator[#]]&/@BernoulliB[2 Range[0,20]] (* _Harvey P. Dale_, Jun 18 2022 *)

%o (PARI) a(n) = my(b=bernfrac(2*n)); abs(numerator(b)-denominator(b)); \\ _Michel Marcus_, Nov 25 2018

%o (GAP) List([0..30],n->AbsInt(NumeratorRat(Bernoulli(2*n))-DenominatorRat(Bernoulli(2*n))));  # _Muniru A Asiru_, Nov 25 2018

%Y Cf. A000367, A002445.

%K nonn

%O 0,2

%A _Juri-Stepan Gerasimov_, Jun 27 2009

%E a(13) corrected by _Paul Curtz_, Sep 07 2009

%E a(15) and a(16) corrected by _R. J. Mathar_, Sep 13 2009

%E Offset 0 from _Amiram Eldar_, Nov 25 2018