Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #21 Apr 14 2023 10:53:32
%S 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,
%T 1425523,0,27298263,0,601580913,0,15116315788,0,429614643067,0,
%U 13711655205344,0,488332318973599,0,19296579341940107,0,841693047573684421,0,40338071854059455479
%N a(n) is the sum of the terms in the continued fraction of the absolute value of B_n, the n-th Bernoulli number.
%C For all odd n >=3, a(n) = 0.
%H Jinyuan Wang, <a href="/A138703/b138703.txt">Table of n, a(n) for n = 0..635</a>
%e 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.
%p 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
%t Table[ ContinuedFraction[ BernoulliB[n] // Abs] // Total, {n, 0, 50}] (* _Jean-François Alcover_, Mar 27 2013 *)
%o (PARI) a(n) = vecsum(contfrac(abs(bernfrac(n)))); \\ _Jinyuan Wang_, Aug 07 2021
%o (Python)
%o from sympy import continued_fraction, bernoulli
%o def A138703(n): return sum(continued_fraction(abs(bernoulli(n)))) # _Chai Wah Wu_, Apr 14 2023
%Y Cf. A027641/A027642, A138701, A138702, A138706.
%K nonn
%O 0,2
%A _Leroy Quet_, Mar 26 2008
%E Extended beyond a(15) by _R. J. Mathar_, Jul 20 2009
%E More terms from _Jean-François Alcover_, Mar 27 2013