A010465 Decimal expansion of square root of 7.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons
• easy

Comments

Continued fraction expansion is 2 followed by {1, 1, 1, 4} repeated. - Harry J. Smith, Jun 01 2009

The convergents to sqrt(7) are given in A041008/A041009. - Wolfdieter Lang, Nov 22 2017

Examples

			2.645751311064590590501615753639260425710259183082450180368334459201...
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• Jason Kimberley, Index of expansions of sqrt(d) in base b.
• R. J. Nemiroff & J. Bonnell, The first 1 million digits of the square root of 7.
• Simon Plouffe, Plouffe's Inverter, sqrt(7) to 100000 digits.
• Index entries for algebraic numbers, degree 2.

Crossrefs

Cf. A010121 (continued fraction), A041008/A041009.

Programs

Magma

SetDefaultRealField(RealField(100)); Sqrt(7); // Vincenzo Librandi, Feb 15 2020

Mathematica

RealDigits[N[Sqrt[7], 200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 21 2011 *)

PARI

default(realprecision, 20080); x=sqrt(7); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010465.txt", n, " ", d));  \\ Harry J. Smith, Jun 01 2009

Formula

Equals 8*cos(Pi/14)*sin(2*Pi/14)*cos(3*Pi/14). - Gerry Martens, Mar 13 2025