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A138703 a(n) = sum of the terms in the continued fraction of the absolute value of B_n, the n-th Bernoulli number. 4
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, 0, 2115074863808199160579, 0, 120866265222965259346062, 0, 7500866746076964366855738 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

Table of n, a(n) for n=0..50.

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 *)

CROSSREFS

Cf. A138701, A138702, A138706.

Sequence in context: A243015 A139717 A202535 * A106458 A213323 A122685

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

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Last modified December 11 08:51 EST 2016. Contains 279052 sequences.