1,1
Continued fraction expansion of (7+sqrt(53))/2 is A010727.
This is the shape of a 7-extension rectangle; see A188640 for definitions. [From Clark Kimberling, Apr 09 2011]
Table of n, a(n) for n=1..105.
Wikipedia, Metallic mean
(7+sqrt(53))/2 = 7.14005494464025913554...
r=7; t = (r + (4+r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
(PARI) (7+sqrt(53))/2 \\ Charles R Greathouse IV, Jul 24 2013
Cf. A010506 (decimal expansion of sqrt(53)), A010727 (all 7's sequence).
Sequence in context: A201585 A089562 A104621 * A048834 A010504 A242132
Adjacent sequences: A176436 A176437 A176438 * A176440 A176441 A176442
cons,nonn
Klaus Brockhaus, Apr 19 2010
approved