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A234255 Decimal expansion of -B(12) = 691/2730, 13th Bernoulli number without sign.

%I A234255 #27 Sep 08 2022 08:46:06
%S A234255 0,2,5,3,1,1,3,5,5,3,1,1,3,5,5,3,1,1,3,5,5,3,1,1,3,5,5,3,1,1,3,5,5,3,
%T A234255 1,1,3,5,5,3,1,1,3,5,5,3,1,1,3,5,5,3,1,1,3,5,5,3,1,1,3,5,5,3,1,1,3,5,
%U A234255 5,3,1,1,3,5,5,3,1,1,3,5,5,3,1,1,3,5,5,3,1,1,3,5,5,3,1,1,3,5,5,3,1,1,3,5,5
%N A234255 Decimal expansion of -B(12) = 691/2730, 13th Bernoulli number without sign.
%C A234255 Essentially of period 6: repeat [5, 3, 1, 1, 3, 5] = A110551(n+3).
%C A234255 691*3663 = 2531133. See A021277.
%C A234255 Seventh part of the constant c=0.6323809537553113569215686274509803711... .
%C A234255 B(24) - B(12) = -86580. See A002882.
%H A234255 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,1).
%F A234255 From _Chai Wah Wu_, Jun 04 2016: (Start)
%F A234255 a(n) = 2*a(n-1) - 2*a(n-2) + a(n-3) for n > 5.
%F A234255 G.f.: x^2*(2 + x - 3*x^2 + 3*x^3)/((1 - x)*(1 - x + x^2)). (End)
%F A234255 From _Wesley Ivan Hurt_, Jun 28 2016: (Start)
%F A234255 a(n) = a(n-6) for n>8.
%F A234255 a(n) = (9 - 6*cos(n*Pi/3) + 2*sqrt(3)*sin(n*Pi/3))/3 for n>2. (End)
%e A234255 0.2531135531135531135531135531135531135531135...
%p A234255 A234255:=n->[5, 3, 1, 1, 3, 5][(n mod 6)+1]: 0,2,seq(A234255(n), n=0..100); # _Wesley Ivan Hurt_, Jun 28 2016
%t A234255 Join[{0},RealDigits[-BernoulliB[12],10,120][[1]]] (* or *) PadRight[{0,2}, 120, {3,5,5,3,1,1}] (* _Harvey P. Dale_, Dec 30 2013 *)
%o A234255 (PARI)
%o A234255 default(realprecision, 120);
%o A234255 -bernfrac(12) + 0. \\ _Rick L. Shepherd_, Jan 15 2014
%o A234255 (Magma) [0,2] cat &cat [[5, 3, 1, 1, 3, 5]^^30]; // _Wesley Ivan Hurt_, Jun 28 2016
%Y A234255 Cf. (A027641 or A164555)/A027642, A000367/A002445, A020793, A021046, A234355, A234356, A112828. B(24).
%Y A234255 Cf. A002882, A110551, A021277.
%K A234255 nonn,easy,cons
%O A234255 1,2
%A A234255 _Paul Curtz_, Dec 22 2013
%E A234255 Offset corrected by and more terms from _Rick L. Shepherd_, Jan 15 2014