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A234255
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Decimal expansion of -B(12) = 691/2730, 13th Bernoulli number without sign.
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1
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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, 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, 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
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OFFSET
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1,2
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COMMENTS
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Essentially of period 6: repeat [5, 3, 1, 1, 3, 5] = A110551(n+3).
Seventh part of the constant c=0.6323809537553113569215686274509803711... .
B(24) - B(12) = -86580. See A002882.
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LINKS
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FORMULA
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a(n) = 2*a(n-1) - 2*a(n-2) + a(n-3) for n > 5.
G.f.: x^2*(2 + x - 3*x^2 + 3*x^3)/((1 - x)*(1 - x + x^2)). (End)
a(n) = a(n-6) for n>8.
a(n) = (9 - 6*cos(n*Pi/3) + 2*sqrt(3)*sin(n*Pi/3))/3 for n>2. (End)
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EXAMPLE
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0.2531135531135531135531135531135531135531135...
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MAPLE
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MATHEMATICA
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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 *)
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PROG
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(PARI)
default(realprecision, 120);
(Magma) [0, 2] cat &cat [[5, 3, 1, 1, 3, 5]^^30]; // Wesley Ivan Hurt, Jun 28 2016
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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