A177037 Decimal expansion of (9 + 2*sqrt(39))/15.

1, 4, 3, 2, 6, 6, 6, 3, 9, 9, 7, 8, 6, 4, 5, 3, 0, 9, 4, 1, 1, 2, 9, 1, 9, 0, 8, 2, 7, 9, 1, 9, 7, 2, 5, 9, 4, 8, 0, 9, 7, 2, 7, 9, 9, 7, 0, 6, 5, 5, 5, 4, 1, 7, 4, 4, 6, 0, 3, 9, 6, 2, 5, 7, 4, 1, 4, 6, 1, 4, 8, 2, 6, 7, 4, 4, 4, 6, 8, 6, 0, 0, 0, 8, 4, 4, 4, 4, 8, 1, 4, 9, 6, 2, 8, 4, 5, 4, 1, 1, 6, 1, 4, 3, 7

Offset

1,2

Comments

Continued fraction expansion of (9 + 2*sqrt(39))/15 is A010883.

The positive solution to 15*x^2 - 18*x - 5 = 0. - Michal Paulovic, Feb 23 2023

Links

Table of n, a(n) for n=1..105.

Formula

Equals sqrt(1/3 + (6/5) * sqrt(1/3 + (6/5) * sqrt(1/3 + (6/5) * ...))). - Michal Paulovic, Feb 23 2023

Example

1.43266639978645309411...

Maple

evalf(3/5 + sqrt(52/75), 100); # Michal Paulovic, Feb 24 2023

Mathematica

RealDigits[(9+2*Sqrt[39])/15, 10, 120][[1]] (* Harvey P. Dale, Feb 12 2013 *)

Prog

(PARI) my(c=(9+2*quadgen(4*39))/15); a_vector(len) = digits(floor(c*10^(len-1)));
a_vector(100) \\ Kevin Ryde, Feb 24 2023

Crossrefs

Cf. A010493 (decimal expansion of sqrt(39)), A010883 (repeat 1, 2, 3, 4).

Sequence in context: A275957 A282539 A021702 * A010651 A286388 A194758

Adjacent sequences: A177034 A177035 A177036 * A177038 A177039 A177040

Keyword

cons,nonn

Author

Klaus Brockhaus, May 01 2010

Status

approved