A227233 The continued fraction of the constant r > sqrt(3) such that the partial quotients equal the integer floor of the powers of r.

1, 1, 3, 5, 9, 16, 29, 52, 92, 163, 287, 507, 893, 1573, 2772, 4884, 8605, 15159, 26705, 47045, 82878, 146003, 257207, 453112, 798230, 1406210, 2477265, 4364097, 7688055, 13543737, 23859456, 42032242, 74046506, 130444746, 229799252, 404828081, 713169314, 1256361635, 2213281654

Offset

0,3

Links

Table of n, a(n) for n=0..38.

Example

This constant r, found in the interval (sqrt(3), 2), satisfies the continued fraction:
r = [1; [r], [r^2], [r^3], [r^4], ..., floor(r^n), ...], more explicitly:
r = [1; 1, 3, 5, 9, 16, 29, 52, 92, 163, 287, 507, 893, 1573, ...] where
r = 1.7616596940944800771133433079549530812923042547055232047896...
See A227232 for another constant that satisfies a continued fraction of the same construction but is found in the interval (1, sqrt(3)).

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. A227232.

Sequence in context: A094980 A295060 A069818 * A054180 A188223 A348125

Adjacent sequences: A227230 A227231 A227232 * A227234 A227235 A227236

Keyword

nonn,cofr

Author

Paul D. Hanna, Jul 03 2013

Status

approved