A010473 Decimal expansion of square root of 17.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons
• easy

Comments

Continued fraction expansion is 4 followed by {8} repeated. - Harry J. Smith, Jun 05 2009

The spiral of Theodorus is an agglomeration of right triangles each having a hypotenuse with a length that is the square root of an integer. The original spiral stops at sqrt(17). - Alonso del Arte, Apr 30 2015

The fundamental algebraic (integer) number in the field Q(sqrt(17)) is (1 + sqrt(17))/2 = A222132. - Wolfdieter Lang, Nov 21 2023

Examples

			4.123105625617660549821409855974077025147199225373620434398633573...
		

References

• James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 275.
• David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 58.

Links

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

Crossrefs

Cf. A040012 (continued fraction), A222132.

Programs

Mathematica

RealDigits[N[Sqrt[17], 100]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 21 2011 *)

PARI

default(realprecision, 20080); x=sqrt(17); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010473.txt", n, " ", d));  \\ Harry J. Smith, Jun 03 2009