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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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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
KEYWORD
nonn,cofr
AUTHOR
Paul D. Hanna, Jul 03 2013
STATUS
approved

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Last modified June 14 13:49 EDT 2024. Contains 373400 sequences. (Running on oeis4.)