A010499 - OEIS

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..20000

Index entries for algebraic numbers, degree 2

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)

EXAMPLE

6.708203932499369089227521006193828706321855078834577172812691736231562...

MATHEMATICA

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

PROG

(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

CROSSREFS

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

Cf. A020802 (reciprocal), A002163, A001622.

Sequence in context: A224238 A227718 A198932 * A218012 A195714 A247043

Adjacent sequences: A010496 A010497 A010498 * A010500 A010501 A010502

KEYWORD

nonn,cons,easy

AUTHOR

N. J. A. Sloane

STATUS

approved