A010473 - OEIS

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

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

OFFSET

1,1

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

REFERENCES

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.

EXAMPLE

4.123105625617660549821409855974077025147199225373620434398633573...

MATHEMATICA

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

PROG

(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

CROSSREFS

Cf. A040012 (continued fraction), A222132.

Sequence in context: A213884 A117021 A222213 * A176041 A131100 A378626

Adjacent sequences: A010470 A010471 A010472 * A010474 A010475 A010476

KEYWORD

nonn,cons,easy

AUTHOR

N. J. A. Sloane

STATUS

approved