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A234255 Decimal expansion of -B(12) = 691/2730, 13th Bernoulli number without sign. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Essentially of period 6: repeat [5, 3, 1, 1, 3, 5] = A110551(n+3).
691*3663 = 2531133. See A021277.
Seventh part of the constant c=0.6323809537553113569215686274509803711... .
B(24) - B(12) = -86580. See A002882.
LINKS
FORMULA
From Chai Wah Wu, Jun 04 2016: (Start)
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)
From Wesley Ivan Hurt, Jun 28 2016: (Start)
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)
EXAMPLE
0.2531135531135531135531135531135531135531135...
MAPLE
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
MATHEMATICA
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 *)
PROG
(PARI)
default(realprecision, 120);
-bernfrac(12) + 0. \\ Rick L. Shepherd, Jan 15 2014
(Magma) [0, 2] cat &cat [[5, 3, 1, 1, 3, 5]^^30]; // Wesley Ivan Hurt, Jun 28 2016
CROSSREFS
Sequence in context: A279536 A269954 A326953 * A062706 A059217 A021802
KEYWORD
nonn,easy,cons
AUTHOR
Paul Curtz, Dec 22 2013
EXTENSIONS
Offset corrected by and more terms from Rick L. Shepherd, Jan 15 2014
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)