The On-Line Encyclopedia of Integer Sequences (OEIS)

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A234255

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

#27 by Charles R Greathouse IV at Thu Sep 08 08:46:06 EDT 2022

PROG

(MAGMAMagma) [0, 2] cat &cat [[5, 3, 1, 1, 3, 5]^^30]; // Wesley Ivan Hurt, Jun 28 2016

Discussion

Thu Sep 08

08:46

OEIS Server: https://oeis.org/edit/global/2944

#26 by Joerg Arndt at Wed Jun 29 02:12:32 EDT 2016

STATUS

reviewed

approved

#25 by Michel Marcus at Tue Jun 28 17:28:39 EDT 2016

STATUS

proposed

reviewed

#24 by Wesley Ivan Hurt at Tue Jun 28 12:40:12 EDT 2016

STATUS

editing

proposed

#23 by Wesley Ivan Hurt at Tue Jun 28 12:39:46 EDT 2016

FORMULA

a(n) = (9 - 6*cos(n*Pi/3) + 2*sqrt(3)*sin(n*Pi/3))/3 for n>2. (End)

#22 by Wesley Ivan Hurt at Tue Jun 28 12:38:59 EDT 2016

NAME

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

COMMENTS

Essentially of period 6: repeat [5, 3, 1, 1, 3, 5 ] = A110551(n+3).

691*3663 = 2531133. See A021277.

LINKS

<a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,1).

FORMULA

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.

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

(MAGMA) [0, 2] cat &cat [[5, 3, 1, 1, 3, 5]^^30]; // Wesley Ivan Hurt, Jun 28 2016

CROSSREFS

Cf. A002882, A110551, A021277.

KEYWORD

nonn,easy,cons

STATUS

approved

editing

#21 by Michel Marcus at Sun Jun 05 02:01:59 EDT 2016

STATUS

reviewed

approved

#20 by Joerg Arndt at Sun Jun 05 01:45:13 EDT 2016

STATUS

proposed

reviewed

#19 by Chai Wah Wu at Sat Jun 04 12:59:00 EDT 2016

STATUS

editing

proposed

#18 by Chai Wah Wu at Sat Jun 04 12:58:38 EDT 2016

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)

STATUS

approved

editing