A138705 a(n) is the number of terms in the continued fraction of the absolute value of B_{2n}, the (2n)-th Bernoulli number.

1, 2, 2, 2, 2, 3, 6, 2, 7, 7, 4, 4, 6, 2, 6, 7, 7, 2, 10, 2, 8, 2, 3, 5, 10, 3, 7, 7, 6, 6, 17, 2, 7, 10, 2, 7, 23, 2, 2, 5, 18, 5, 16, 2, 10, 14, 6, 2, 18, 2, 9, 5, 7, 6, 18, 4, 15, 2, 6, 2, 17, 2, 2, 15, 7, 9, 12, 2, 8, 11, 12, 2, 21, 2, 6, 14, 2, 4, 23, 2

Offset

0,2

Comments

The continued fraction terms being counted include the initial 0, if there is one.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Example

The 12th Bernoulli number is -691/2730. Now 691/2730 has the continued fraction 0 + 1/(3 + 1/(1 + 1/(19 + 1/(3 + 1/11)))), which has 6 terms (including the zero). So a(6) = 6.

Mathematica

Table[Length[ContinuedFraction[Abs[BernoulliB[2*n]]]], {n, 0, 100}] (* Vaclav Kotesovec, Oct 03 2019 *)

Prog

(PARI) a(n) = #contfrac(abs(bernfrac(2*n))); \\ Jinyuan Wang, Aug 07 2021
(Python)
from sympy import continued_fraction, bernoulli
def A138705(n): return len(continued_fraction(abs(bernoulli(n<<1)))) # Chai Wah Wu, Apr 14 2023

Crossrefs

Cf. A027641/A027642, A138704, A138706.

Sequence in context: A098133 A138185 A225941 * A333528 A319187 A248780

Adjacent sequences: A138702 A138703 A138704 * A138706 A138707 A138708

Keyword

nonn

Author

Leroy Quet, Mar 26 2008

Extensions

a(8)-a(70) from Lars Blomberg, Mar 16 2012

Status

approved