A138702 a(n) = number of terms in the continued fraction of the absolute value of B_n, the n-th Bernoulli number.

1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 6, 1, 2, 1, 7, 1, 7, 1, 4, 1, 4, 1, 6, 1, 2, 1, 6, 1, 7, 1, 7, 1, 2, 1, 10, 1, 2, 1, 8, 1, 2, 1, 3, 1, 5, 1, 10, 1, 3, 1, 7, 1, 7, 1, 6, 1, 6, 1, 17, 1, 2, 1, 7, 1, 10, 1, 2, 1, 7, 1, 23, 1, 2, 1, 2, 1, 5, 1, 18, 1, 5, 1, 16, 1, 2, 1, 10, 1, 14, 1, 6, 1, 2, 1, 18, 1, 2, 1

Offset

0,2

Comments

The continued fraction terms being counted include the initial 0, if there is one. (a(n), for all odd n >= 3, is 1.)

Links

Antti Karttunen, Table of n, a(n) for n = 0..16383

Example

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(12) = 6.

Prog

(PARI)
lcf(x)=local(r); r=1; while(1, x-=floor(x); if(x==0, return(r)); x=1/x; r++)
a(n)=lcf(abs(bernfrac(n))) \\ Franklin T. Adams-Watters, May 14 2010

Crossrefs

Cf. A138701, A138703.

Sequence in context: A319981 A052005 A346707 * A344339 A348364 A279620

Adjacent sequences: A138699 A138700 A138701 * A138703 A138704 A138705

Keyword

nonn

Author

Leroy Quet, Mar 26 2008

Extensions

More terms from Franklin T. Adams-Watters, May 14 2010

Status

approved