A010499 Decimal expansion of square root of 45.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons
• easy

Comments

Continued fraction expansion is 6 followed by {1, 2, 2, 2, 1, 12} repeated (A010135). - Harry J. Smith, Jun 06 2009

Examples

			6.708203932499369089227521006193828706321855078834577172812691736231562...
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• Index entries for algebraic numbers, degree 2

Crossrefs

Cf. A010135 (continued fraction), A248271 (Egyptian fractions).

Cf. A020802 (reciprocal), A002163, A001622.

Programs

Mathematica

RealDigits[N[Sqrt[45],200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 24 2011 *)

PARI

default(realprecision, 20080); x=sqrt(45); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010499.txt", n, " ", d));  \\ Harry J. Smith, Jun 06 2009

Formula

Equals 3 * A002163. - Amiram Eldar, May 25 2023

From Andrea Pinos, Nov 01 2023: (Start)

Equals phi^4 - 1/phi^4 where phi = A001622 is the golden ratio.

Equals 2*sinh(4*log(phi)). (End)