A010547 Decimal expansion of square root of 96.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Comments

Continued fraction expansion is 9 followed by {1, 3, 1, 18} repeated. - Harry J. Smith, Jun 11 2009

This differs only by offset from 2*(6^(1/2))/5 = 0.9797958971132712392789... as used in Theorem 5, equation 1.8, p.4 of Cao. - Jonathan Vos Post, Apr 29 2010

Examples

			9.797958971132712392789136298823565567863789922626680513730770269003841...
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• Zhenwei Cao and Alexander Elgart, On efficiency of Hamiltonian--based quantum computation for low-rank matrices, arXiv:1004.4911 [math-ph], 2010-2012.
• Index entries for algebraic numbers, degree 2.

Crossrefs

Cf. A010167 (continued fraction).

Programs

Mathematica

RealDigits[N[96^(1/2),200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jan 24 2012 *)

PARI

{ default(realprecision, 20080); x=sqrt(96); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010547.txt", n, " ", d)); } \\ Harry J. Smith, Jun 11 2009

Formula

Equals 4*A010464. - R. J. Mathar, Feb 03 2025

Extensions

Final digits of sequence corrected using the b-file. - N. J. A. Sloane, Aug 30 2009