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

Author

Leroy Quet, Mar 26 2008

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A027641/A027642, A138704, A138706.

Programs

Mathematica

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

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

Extensions

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