OFFSET
0,3
EXAMPLE
This constant r, found in the interval (1, sqrt(3)), satisfies the continued fraction:
r = [1; [r], [r^2], [r^3], [r^4], ..., floor(r^n), ...], more explicitly:
r = [1; 1, 2, 4, 8, 13, 23, 39, 67, 113, 191, 324, 548, 928, ...] where
r = 1.691595419636107091520608953850126286827042452195819302381...
See A227233 for another constant that satisfies a continued fraction of the same construction but is found in the interval (sqrt(3), 2).
PROG
(PARI) {a(n)=local(r=sqrt(3)-1/10^4); for(i=1, 10, M=contfracpnqn(vector(2*n+2, k, floor(r^(k-1)))); r=M[1, 1]/M[2, 1]*1.); floor(r^n)}
for(n=0, 40, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn,cofr
AUTHOR
Paul D. Hanna, Jul 03 2013
STATUS
approved