A227232 The continued fraction of the positive constant r < sqrt(3) such that the partial quotients equal the integer floor of the powers of r.

1, 1, 2, 4, 8, 13, 23, 39, 67, 113, 191, 324, 548, 928, 1570, 2657, 4495, 7603, 12862, 21758, 36806, 62262, 105322, 178163, 301381, 509814, 862400, 1458832, 2467754, 4174442, 7061468, 11945147, 20206356, 34180980, 57820390, 97808707, 165452761, 279879132, 473442259, 800872756

Offset

0,3

Links

Table of n, a(n) for n=0..39.

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

Cf. A227233.

Sequence in context: A336980 A164417 A258600 * A164408 A303852 A096573

Adjacent sequences: A227229 A227230 A227231 * A227233 A227234 A227235

Keyword

nonn,cofr

Author

Paul D. Hanna, Jul 03 2013

Status

approved