A234356 -id:A234356 - cp's OEIS frontend

A234355 Decimal expansion of B(16) = -3617/510, the 16th Bernoulli number.

7, 0, 9, 2, 1, 5, 6, 8, 6, 2, 7, 4, 5, 0, 9, 8, 0, 3, 9, 2, 1, 5, 6, 8, 6, 2, 7, 4, 5, 0, 9, 8, 0, 3, 9, 2, 1, 5, 6, 8, 6, 2, 7, 4, 5, 0, 9, 8, 0, 3, 9, 2, 1, 5, 6, 8, 6, 2, 7, 4, 5, 0, 9, 8, 0, 3, 9, 2, 1, 5, 6, 8, 6, 2, 7, 4, 5, 0, 9, 8, 0, 3, 9, 2, 1, 5, 6, 8, 6, 2, 7, 4, 5, 0, 9, 8, 0, 3, 9, 2, 1

Offset: 1

Jean-François Alcover and Paul Curtz, Dec 24 2013

B(6), B(16) and B(18) are the first three Bernoulli numbers whose index is equal to their decimal expansion periodic length, B(16) and B(18) being the smallest such pair of consecutive even-indexed Bernoulli numbers.

			-7.092156862745098039215686274509803...

Cf. A021046 (B(6)), A234356 (B(18)).

RealDigits[BernoulliB[16], 10, 100] // First

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

Original entry on oeis.org

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

Offset: 1

Paul Curtz, Dec 22 2013

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.

			0.2531135531135531135531135531135531135531135...

Index entries for linear recurrences with constant coefficients, signature (2,-2,1).

Cf. (A027641 or A164555)/A027642, A000367/A002445, A020793, A021046, A234355, A234356, A112828. B(24).

Cf. A002882, A110551, A021277.

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

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

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 *)

default(realprecision, 120);
-bernfrac(12) + 0. \\ Rick L. Shepherd, Jan 15 2014

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)

Offset corrected by and more terms from Rick L. Shepherd, Jan 15 2014

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A234355 Decimal expansion of B(16) = -3617/510, the 16th Bernoulli number.

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

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