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