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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, 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 (list; graph; refs; listen; history; text; internal format)
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: A233274 A164417 A258600 * A303852 A096573 A227910

Adjacent sequences:  A227229 A227230 A227231 * A227233 A227234 A227235

KEYWORD

nonn,cofr

AUTHOR

Paul D. Hanna, Jul 03 2013

STATUS

approved

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Last modified October 19 03:34 EDT 2019. Contains 328211 sequences. (Running on oeis4.)