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A176439 Decimal expansion of (7+sqrt(53))/2. 9
7, 1, 4, 0, 0, 5, 4, 9, 4, 4, 6, 4, 0, 2, 5, 9, 1, 3, 5, 5, 4, 8, 6, 5, 1, 2, 4, 5, 7, 6, 3, 5, 1, 6, 3, 9, 6, 8, 8, 8, 8, 3, 4, 8, 4, 1, 2, 8, 8, 2, 3, 8, 7, 1, 9, 1, 8, 9, 0, 9, 0, 8, 9, 5, 6, 4, 2, 0, 5, 7, 8, 6, 9, 3, 1, 2, 4, 5, 2, 5, 9, 1, 6, 6, 4, 7, 8, 9, 7, 0, 4, 5, 4, 0, 4, 6, 3, 3, 7, 6, 0, 9, 6, 3, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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]
c^n = c * A054413(n-1) + A054413(n-2), where c = (7+sqrt(53))/2. - Gary W. Adamson, Apr 14 2024
LINKS
Wikipedia, Metallic mean
FORMULA
Equals lim_{n->oo} S(n, sqrt(53))/S(n-1, sqrt(53)), with the S-Chebyshev polynomials (see A049310). - Wolfdieter Lang, Nov 15 2023
Positive solution of x^2 - 7*x - 1 = 0. - Hugo Pfoertner, Apr 14 2024
EXAMPLE
(7+sqrt(53))/2 = 7.14005494464025913554...
MATHEMATICA
r=7; t = (r + (4+r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
PROG
(PARI) (7+sqrt(53))/2 \\ Charles R Greathouse IV, Jul 24 2013
CROSSREFS
Cf. A010506 (decimal expansion of sqrt(53)), A010727 (all 7's sequence).
Cf. A049310.
Sequence in context: A089562 A104621 A331900 * A048834 A010504 A242132
KEYWORD
nonn,cons,easy
AUTHOR
Klaus Brockhaus, Apr 19 2010
STATUS
approved

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Last modified June 22 22:41 EDT 2024. Contains 373629 sequences. (Running on oeis4.)