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

Author

Leroy Quet, Mar 26 2008

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A138701, A138703.

Programs

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

Extensions

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