|
|
COMMENTS
| Convergents A119811: [2/1,7/3,72/31,9511/4095,1246930216/536870911,...], where the denominators of the convergents are equal to [2^A000129(n-1)-1] and A000129 is the Pell numbers. The number of digits in these partial quotients are (beginning at n=1): [1,1,2,3,6,13,30,72,174,420,1013,2445,5901,14246,34391,83027,...].
|
|
|
EXAMPLE
| c = 2.32258852258806773012144068278798408011950250800432925665718...
The partial quotients start:
a(1) = 2^1; a(2) = 2^1 + 2^0; a(3) = 2^3 + 2^1;
a(4) = 2^7 + 2^2; a(5) = 2^17 + 2^5; a(6) = 2^41 + 2^12;
and continue as a(n) = 2^A001333(n-1) + 2^A000129(n-2) where
A001333(n) = ( (1+sqrt(2))^n + (1-sqrt(2))^n )/2;
A000129(n) = ( (1+sqrt(2))^n - (1-sqrt(2))^n )/(2*sqrt(2)).
|
