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A162173 Absolute difference of numerator and denominator of Bernoulli(2*n), n >= 0.

%I A162173 #25 Oct 07 2024 01:17:24
%S A162173 0,5,31,41,31,61,3421,1,4127,43069,174941,854375,236366821,8553097,
%T A162173 23749461899,8615841261683,7709321041727,2577687858361,
%U A162173 26315271553055396563,2929993913841553,261082718496449135581
%N A162173 Absolute difference of numerator and denominator of Bernoulli(2*n), n >= 0.
%H A162173 Muniru A Asiru, <a href="/A162173/b162173.txt">Table of n, a(n) for n = 0..310</a>
%F A162173 a(n) = abs(A000367(n) - A002445(n)).
%e A162173 a(0) = abs(1 - 1) = 0.
%e A162173 a(1) = abs(1 - 6) = 5.
%e A162173 a(2) = abs(-1 - 30) = 31.
%p A162173 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 A162173 a[n_] := Abs[Numerator[BernoulliB[2n]] - Denominator[BernoulliB[2n]]]; Array[a, 20, 0] (* _Amiram Eldar_, Nov 25 2018 *)
%t A162173 Abs[Denominator[#]-Numerator[#]]&/@BernoulliB[2 Range[0,20]] (* _Harvey P. Dale_, Jun 18 2022 *)
%o A162173 (PARI) a(n) = my(b=bernfrac(2*n)); abs(numerator(b)-denominator(b)); \\ _Michel Marcus_, Nov 25 2018
%o A162173 (GAP) List([0..30],n->AbsInt(NumeratorRat(Bernoulli(2*n))-DenominatorRat(Bernoulli(2*n))));  # _Muniru A Asiru_, Nov 25 2018
%Y A162173 Cf. A000367, A002445.
%K A162173 nonn
%O A162173 0,2
%A A162173 _Juri-Stepan Gerasimov_, Jun 27 2009
%E A162173 a(13) corrected by _Paul Curtz_, Sep 07 2009
%E A162173 a(15) and a(16) corrected by _R. J. Mathar_, Sep 13 2009
%E A162173 Offset 0 from _Amiram Eldar_, Nov 25 2018