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
Keywords
Examples
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.
Links
- Jinyuan Wang, Table of n, a(n) for n = 0..635
Programs
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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
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Mathematica
Table[ ContinuedFraction[ BernoulliB[n] // Abs] // Total, {n, 0, 50}] (* Jean-François Alcover, Mar 27 2013 *) -
PARI
a(n) = vecsum(contfrac(abs(bernfrac(n)))); \\ Jinyuan Wang, Aug 07 2021
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Python
from sympy import continued_fraction, bernoulli def A138703(n): return sum(continued_fraction(abs(bernoulli(n)))) # Chai Wah Wu, Apr 14 2023
Extensions
Extended beyond a(15) by R. J. Mathar, Jul 20 2009
More terms from Jean-François Alcover, Mar 27 2013
Comments