A138703 a(n) is the sum of the terms in the continued fraction of the absolute value of B_n, the n-th Bernoulli number.

1, 2, 6, 0, 30, 0, 42, 0, 30, 0, 18, 0, 37, 0, 7, 0, 28, 0, 96, 0, 559, 0, 6210, 0, 86617, 0, 1425523, 0, 27298263, 0, 601580913, 0, 15116315788, 0, 429614643067, 0, 13711655205344, 0, 488332318973599, 0, 19296579341940107, 0, 841693047573684421, 0, 40338071854059455479

Offset

0,2

Comments

For all odd n >=3, a(n) = 0.

Links

Jinyuan Wang, Table of n, a(n) for n = 0..635

Example

The 12th Bernoulli number is -691/2730. Now 691/2730 = the continued fraction 0 + 1/(3 + 1/(1 + 1/(19 + 1/(3 + 1/11)))). So a(12) = 0 + 3 + 1 + 19 + 3 + 11 = 37.

Maple

A138701row := proc(n) local B; B := abs(bernoulli(n)) ; numtheory[cfrac](B, 20, 'quotients') ; end: A138703 := proc(n) add(c, c=A138701row(n)) ; end: seq(op(A138703(n)), n=0..80) ; # R. J. Mathar, Jul 20 2009

Mathematica

Table[ ContinuedFraction[ BernoulliB[n] // Abs] // Total, {n, 0, 50}] (* Jean-François Alcover, Mar 27 2013 *)

Prog

(PARI) a(n) = vecsum(contfrac(abs(bernfrac(n)))); \\ Jinyuan Wang, Aug 07 2021
(Python)
from sympy import continued_fraction, bernoulli
def A138703(n): return sum(continued_fraction(abs(bernoulli(n)))) # Chai Wah Wu, Apr 14 2023

Crossrefs

Cf. A027641/A027642, A138701, A138702, A138706.

Sequence in context: A139717 A285119 A202535 * A106458 A354351 A213323

Adjacent sequences: A138700 A138701 A138702 * A138704 A138705 A138706

Keyword

nonn

Author

Leroy Quet, Mar 26 2008

Extensions

Extended beyond a(15) by R. J. Mathar, Jul 20 2009

More terms from Jean-François Alcover, Mar 27 2013

Status

approved