OFFSET
1,4
COMMENTS
The limits of the continued fraction is Cd = 0.6123687534182316423985073896748729172179677660718454489694806870..., i.e. the number associated to the sequence of number of distinct primes dividing n.
EXAMPLE
a[1]=d[1]=0 (d[1] is the first element of A001221, i.e. the number of distinct primes dividing 1).
a[2]=d[2]*a[1]+1=0*1+1=1;
a[3]=d[3]*a[2]+a[1]=1*1+0=1.
MAPLE
a:=proc(N) # A is numerator of the continued fraction # B is denominator of the continued fraction # d is the sequence of the number of divisors of a number (A001221), d[1] is the first element. A[1]:=d[1]; A[2]:=d[2]*A[1]+1; B[1]:=1; B[2]:=d[2]*B[1]; for n from 2 by 1 to N-1 do A[n+1]:=d[n+1]*A[n]+A[n-1]; B[n+1]:=d[n+1]*B[n]+B[n-1]; od; end:
CROSSREFS
KEYWORD
frac,nonn
AUTHOR
Giorgio Balzarotti and Paolo P. Lava, Dec 19 2005
STATUS
approved