OFFSET
1,3
COMMENTS
The number of digits in these numerators are (beginning at n=2): [1,1,3,6,13,30,72,174,420,1013,2444,5901,14245,34391,83027,...].
EXAMPLE
c = 0.858267656461002055792260308433375148664905190083506778667684867..
Convergents begin:
[0/1, 1/1, 6/7, 109/127, 112494/131071, 1887350536045/2199023255551,..]
where the denominators of the convergents equal [2^A001333(n-1)-1]:
[1,1,7,127,131071,2199023255551,633825300114114700748351602687,...]
and A001333 is numerators of continued fraction convergents to sqrt(2).
PROG
(PARI) {a(n)=local(M=contfracpnqn(vector(n, k, if(k==1, 0, if(k==2, 1, 4^round(((1+sqrt(2))^(k-2)+(1-sqrt(2))^(k-2))/(2*sqrt(2))) +if(k==3, 2, 2^round(((1+sqrt(2))^(k-3)-(1-sqrt(2))^(k-3))/2))))))); return(M[1, 1])}
CROSSREFS
KEYWORD
frac,nonn
AUTHOR
Paul D. Hanna, May 26 2006
STATUS
approved