A010499 - OEIS

%I #41 Nov 02 2023 23:42:00

%S 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,

%T 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,

%U 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

%N Decimal expansion of square root of 45.

%C Continued fraction expansion is 6 followed by {1, 2, 2, 2, 1, 12} repeated (A010135). - _Harry J. Smith_, Jun 06 2009

%H Harry J. Smith, <a href="/A010499/b010499.txt">Table of n, a(n) for n = 1..20000</a>

%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>

%F Equals 3 * A002163. - _Amiram Eldar_, May 25 2023

%F From _Andrea Pinos_, Nov 01 2023: (Start)

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

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

%e 6.708203932499369089227521006193828706321855078834577172812691736231562...

%t RealDigits[N[Sqrt[45],200]][[1]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 24 2011 *)

%o (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

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

%Y Cf. A020802 (reciprocal), A002163, A001622.

%K nonn,cons,easy

%O 1,1

%A _N. J. A. Sloane_